2188 lines
66 KiB
C++
2188 lines
66 KiB
C++
//========= Copyright Valve Corporation, All rights reserved. ============//
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//
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// Purpose:
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//
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//===========================================================================//
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#ifndef MATH_LIB_H
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#define MATH_LIB_H
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#include <math.h>
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#include "minmax.h"
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#include "tier0/basetypes.h"
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#include "tier0/commonmacros.h"
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#include "mathlib/vector.h"
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#include "mathlib/vector2d.h"
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#include "tier0/dbg.h"
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#include "mathlib/math_pfns.h"
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#if defined(__i386__) || defined(_M_IX86)
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// For MMX intrinsics
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#include <xmmintrin.h>
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#endif
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// XXX remove me
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#undef clamp
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// Uncomment this to enable FP exceptions in parts of the code.
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// This can help track down FP bugs. However the code is not
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// FP exception clean so this not a turnkey operation.
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//#define FP_EXCEPTIONS_ENABLED
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#ifdef FP_EXCEPTIONS_ENABLED
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#include <float.h> // For _clearfp and _controlfp_s
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#endif
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// FPExceptionDisabler and FPExceptionEnabler taken from my blog post
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// at http://www.altdevblogaday.com/2012/04/20/exceptional-floating-point/
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// Declare an object of this type in a scope in order to suppress
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// all floating-point exceptions temporarily. The old exception
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// state will be reset at the end.
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class FPExceptionDisabler
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{
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public:
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#ifdef FP_EXCEPTIONS_ENABLED
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FPExceptionDisabler();
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~FPExceptionDisabler();
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private:
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unsigned int mOldValues;
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#else
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FPExceptionDisabler() {}
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~FPExceptionDisabler() {}
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#endif
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private:
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// Make the copy constructor and assignment operator private
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// and unimplemented to prohibit copying.
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FPExceptionDisabler(const FPExceptionDisabler&);
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FPExceptionDisabler& operator=(const FPExceptionDisabler&);
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};
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// Declare an object of this type in a scope in order to enable a
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// specified set of floating-point exceptions temporarily. The old
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// exception state will be reset at the end.
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// This class can be nested.
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class FPExceptionEnabler
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{
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public:
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// Overflow, divide-by-zero, and invalid-operation are the FP
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// exceptions most frequently associated with bugs.
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#ifdef FP_EXCEPTIONS_ENABLED
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FPExceptionEnabler(unsigned int enableBits = _EM_OVERFLOW | _EM_ZERODIVIDE | _EM_INVALID);
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~FPExceptionEnabler();
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private:
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unsigned int mOldValues;
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#else
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FPExceptionEnabler(unsigned int enableBits = 0)
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{
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}
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~FPExceptionEnabler()
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{
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}
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#endif
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private:
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// Make the copy constructor and assignment operator private
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// and unimplemented to prohibit copying.
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FPExceptionEnabler(const FPExceptionEnabler&);
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FPExceptionEnabler& operator=(const FPExceptionEnabler&);
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};
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#ifdef DEBUG // stop crashing edit-and-continue
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FORCEINLINE float clamp( float val, float minVal, float maxVal )
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{
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if ( maxVal < minVal )
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return maxVal;
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else if( val < minVal )
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return minVal;
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else if( val > maxVal )
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return maxVal;
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else
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return val;
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}
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#else // DEBUG
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FORCEINLINE float clamp( float val, float minVal, float maxVal )
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{
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#if defined(__i386__) || defined(_M_IX86)
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_mm_store_ss( &val,
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_mm_min_ss(
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_mm_max_ss(
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_mm_load_ss(&val),
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_mm_load_ss(&minVal) ),
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_mm_load_ss(&maxVal) ) );
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#else
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val = fpmax(minVal, val);
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val = fpmin(maxVal, val);
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#endif
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return val;
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}
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#endif // DEBUG
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//
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// Returns a clamped value in the range [min, max].
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//
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template< class T >
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inline T clamp( T const &val, T const &minVal, T const &maxVal )
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{
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if ( maxVal < minVal )
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return maxVal;
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else if( val < minVal )
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return minVal;
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else if( val > maxVal )
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return maxVal;
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else
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return val;
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}
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// plane_t structure
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// !!! if this is changed, it must be changed in asm code too !!!
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// FIXME: does the asm code even exist anymore?
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// FIXME: this should move to a different file
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struct cplane_t
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{
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Vector normal;
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float dist;
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byte type; // for fast side tests
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byte signbits; // signx + (signy<<1) + (signz<<1)
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byte pad[2];
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#ifdef VECTOR_NO_SLOW_OPERATIONS
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cplane_t() {}
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private:
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// No copy constructors allowed if we're in optimal mode
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cplane_t(const cplane_t& vOther);
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#endif
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};
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// structure offset for asm code
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#define CPLANE_NORMAL_X 0
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#define CPLANE_NORMAL_Y 4
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#define CPLANE_NORMAL_Z 8
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#define CPLANE_DIST 12
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#define CPLANE_TYPE 16
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#define CPLANE_SIGNBITS 17
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#define CPLANE_PAD0 18
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#define CPLANE_PAD1 19
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// 0-2 are axial planes
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#define PLANE_X 0
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#define PLANE_Y 1
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#define PLANE_Z 2
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// 3-5 are non-axial planes snapped to the nearest
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#define PLANE_ANYX 3
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#define PLANE_ANYY 4
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#define PLANE_ANYZ 5
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//-----------------------------------------------------------------------------
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// Frustum plane indices.
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// WARNING: there is code that depends on these values
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//-----------------------------------------------------------------------------
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enum
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{
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FRUSTUM_RIGHT = 0,
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FRUSTUM_LEFT = 1,
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FRUSTUM_TOP = 2,
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FRUSTUM_BOTTOM = 3,
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FRUSTUM_NEARZ = 4,
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FRUSTUM_FARZ = 5,
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FRUSTUM_NUMPLANES = 6
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};
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extern int SignbitsForPlane( cplane_t *out );
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class Frustum_t
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{
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public:
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void SetPlane( int i, int nType, const Vector &vecNormal, float dist )
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{
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m_Plane[i].normal = vecNormal;
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m_Plane[i].dist = dist;
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m_Plane[i].type = nType;
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m_Plane[i].signbits = SignbitsForPlane( &m_Plane[i] );
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m_AbsNormal[i].Init( fabs(vecNormal.x), fabs(vecNormal.y), fabs(vecNormal.z) );
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}
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inline const cplane_t *GetPlane( int i ) const { return &m_Plane[i]; }
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inline const Vector &GetAbsNormal( int i ) const { return m_AbsNormal[i]; }
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private:
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cplane_t m_Plane[FRUSTUM_NUMPLANES];
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Vector m_AbsNormal[FRUSTUM_NUMPLANES];
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};
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// Computes Y fov from an X fov and a screen aspect ratio + X from Y
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float CalcFovY( float flFovX, float flScreenAspect );
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float CalcFovX( float flFovY, float flScreenAspect );
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// Generate a frustum based on perspective view parameters
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// NOTE: FOV is specified in degrees, as the *full* view angle (not half-angle)
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void GeneratePerspectiveFrustum( const Vector& origin, const QAngle &angles, float flZNear, float flZFar, float flFovX, float flAspectRatio, Frustum_t &frustum );
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void GeneratePerspectiveFrustum( const Vector& origin, const Vector &forward, const Vector &right, const Vector &up, float flZNear, float flZFar, float flFovX, float flFovY, Frustum_t &frustum );
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// Cull the world-space bounding box to the specified frustum.
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bool R_CullBox( const Vector& mins, const Vector& maxs, const Frustum_t &frustum );
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bool R_CullBoxSkipNear( const Vector& mins, const Vector& maxs, const Frustum_t &frustum );
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struct matrix3x4_t
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{
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matrix3x4_t() {}
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matrix3x4_t(
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float m00, float m01, float m02, float m03,
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float m10, float m11, float m12, float m13,
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float m20, float m21, float m22, float m23 )
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{
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m_flMatVal[0][0] = m00; m_flMatVal[0][1] = m01; m_flMatVal[0][2] = m02; m_flMatVal[0][3] = m03;
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m_flMatVal[1][0] = m10; m_flMatVal[1][1] = m11; m_flMatVal[1][2] = m12; m_flMatVal[1][3] = m13;
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m_flMatVal[2][0] = m20; m_flMatVal[2][1] = m21; m_flMatVal[2][2] = m22; m_flMatVal[2][3] = m23;
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}
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//-----------------------------------------------------------------------------
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// Creates a matrix where the X axis = forward
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// the Y axis = left, and the Z axis = up
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//-----------------------------------------------------------------------------
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void Init( const Vector& xAxis, const Vector& yAxis, const Vector& zAxis, const Vector &vecOrigin )
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{
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m_flMatVal[0][0] = xAxis.x; m_flMatVal[0][1] = yAxis.x; m_flMatVal[0][2] = zAxis.x; m_flMatVal[0][3] = vecOrigin.x;
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m_flMatVal[1][0] = xAxis.y; m_flMatVal[1][1] = yAxis.y; m_flMatVal[1][2] = zAxis.y; m_flMatVal[1][3] = vecOrigin.y;
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m_flMatVal[2][0] = xAxis.z; m_flMatVal[2][1] = yAxis.z; m_flMatVal[2][2] = zAxis.z; m_flMatVal[2][3] = vecOrigin.z;
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}
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//-----------------------------------------------------------------------------
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// Creates a matrix where the X axis = forward
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// the Y axis = left, and the Z axis = up
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//-----------------------------------------------------------------------------
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matrix3x4_t( const Vector& xAxis, const Vector& yAxis, const Vector& zAxis, const Vector &vecOrigin )
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{
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Init( xAxis, yAxis, zAxis, vecOrigin );
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}
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inline void Invalidate( void )
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{
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for (int i = 0; i < 3; i++)
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{
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for (int j = 0; j < 4; j++)
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{
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m_flMatVal[i][j] = VEC_T_NAN;
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}
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}
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}
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float *operator[]( int i ) { Assert(( i >= 0 ) && ( i < 3 )); return m_flMatVal[i]; }
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const float *operator[]( int i ) const { Assert(( i >= 0 ) && ( i < 3 )); return m_flMatVal[i]; }
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float *Base() { return &m_flMatVal[0][0]; }
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const float *Base() const { return &m_flMatVal[0][0]; }
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float m_flMatVal[3][4];
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};
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#ifndef M_PI
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#define M_PI 3.14159265358979323846 // matches value in gcc v2 math.h
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#endif
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#define M_PI_F ((float)(M_PI)) // Shouldn't collide with anything.
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// NJS: Inlined to prevent floats from being autopromoted to doubles, as with the old system.
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#ifndef RAD2DEG
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#define RAD2DEG( x ) ( (float)(x) * (float)(180.f / M_PI_F) )
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#endif
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#ifndef DEG2RAD
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#define DEG2RAD( x ) ( (float)(x) * (float)(M_PI_F / 180.f) )
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#endif
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// Used to represent sides of things like planes.
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#define SIDE_FRONT 0
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#define SIDE_BACK 1
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#define SIDE_ON 2
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#define SIDE_CROSS -2 // necessary for polylib.c
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#define ON_VIS_EPSILON 0.01 // necessary for vvis (flow.c) -- again look into moving later!
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#define EQUAL_EPSILON 0.001 // necessary for vbsp (faces.c) -- should look into moving it there?
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extern bool s_bMathlibInitialized;
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extern const Vector vec3_origin;
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extern const QAngle vec3_angle;
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extern const Quaternion quat_identity;
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extern const Vector vec3_invalid;
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extern const int nanmask;
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#define IS_NAN(x) (((*(int *)&x)&nanmask)==nanmask)
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FORCEINLINE vec_t DotProduct(const vec_t *v1, const vec_t *v2)
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{
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return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
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}
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FORCEINLINE void VectorSubtract(const vec_t *a, const vec_t *b, vec_t *c)
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{
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c[0]=a[0]-b[0];
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c[1]=a[1]-b[1];
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c[2]=a[2]-b[2];
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}
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FORCEINLINE void VectorAdd(const vec_t *a, const vec_t *b, vec_t *c)
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{
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c[0]=a[0]+b[0];
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c[1]=a[1]+b[1];
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c[2]=a[2]+b[2];
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}
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FORCEINLINE void VectorCopy(const vec_t *a, vec_t *b)
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{
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b[0]=a[0];
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b[1]=a[1];
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b[2]=a[2];
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}
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FORCEINLINE void VectorClear(vec_t *a)
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{
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a[0]=a[1]=a[2]=0;
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}
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FORCEINLINE float VectorMaximum(const vec_t *v)
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{
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return max( v[0], max( v[1], v[2] ) );
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}
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FORCEINLINE float VectorMaximum(const Vector& v)
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{
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return max( v.x, max( v.y, v.z ) );
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}
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FORCEINLINE void VectorScale (const float* in, vec_t scale, float* out)
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{
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out[0] = in[0]*scale;
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out[1] = in[1]*scale;
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out[2] = in[2]*scale;
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}
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// Cannot be forceinline as they have overloads:
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inline void VectorFill(vec_t *a, float b)
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{
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a[0]=a[1]=a[2]=b;
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}
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inline void VectorNegate(vec_t *a)
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{
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a[0]=-a[0];
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a[1]=-a[1];
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a[2]=-a[2];
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}
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//#define VectorMaximum(a) ( max( (a)[0], max( (a)[1], (a)[2] ) ) )
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#define Vector2Clear(x) {(x)[0]=(x)[1]=0;}
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#define Vector2Negate(x) {(x)[0]=-((x)[0]);(x)[1]=-((x)[1]);}
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#define Vector2Copy(a,b) {(b)[0]=(a)[0];(b)[1]=(a)[1];}
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#define Vector2Subtract(a,b,c) {(c)[0]=(a)[0]-(b)[0];(c)[1]=(a)[1]-(b)[1];}
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#define Vector2Add(a,b,c) {(c)[0]=(a)[0]+(b)[0];(c)[1]=(a)[1]+(b)[1];}
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#define Vector2Scale(a,b,c) {(c)[0]=(b)*(a)[0];(c)[1]=(b)*(a)[1];}
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// NJS: Some functions in VBSP still need to use these for dealing with mixing vec4's and shorts with vec_t's.
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// remove when no longer needed.
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#define VECTOR_COPY( A, B ) do { (B)[0] = (A)[0]; (B)[1] = (A)[1]; (B)[2]=(A)[2]; } while(0)
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#define DOT_PRODUCT( A, B ) ( (A)[0]*(B)[0] + (A)[1]*(B)[1] + (A)[2]*(B)[2] )
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FORCEINLINE void VectorMAInline( const float* start, float scale, const float* direction, float* dest )
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{
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dest[0]=start[0]+direction[0]*scale;
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dest[1]=start[1]+direction[1]*scale;
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dest[2]=start[2]+direction[2]*scale;
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}
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FORCEINLINE void VectorMAInline( const Vector& start, float scale, const Vector& direction, Vector& dest )
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{
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dest.x=start.x+direction.x*scale;
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dest.y=start.y+direction.y*scale;
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dest.z=start.z+direction.z*scale;
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}
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FORCEINLINE void VectorMA( const Vector& start, float scale, const Vector& direction, Vector& dest )
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{
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VectorMAInline(start, scale, direction, dest);
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}
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FORCEINLINE void VectorMA( const float * start, float scale, const float *direction, float *dest )
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{
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VectorMAInline(start, scale, direction, dest);
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}
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int VectorCompare (const float *v1, const float *v2);
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inline float VectorLength(const float *v)
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{
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return FastSqrt( v[0]*v[0] + v[1]*v[1] + v[2]*v[2] + FLT_EPSILON );
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}
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void CrossProduct (const float *v1, const float *v2, float *cross);
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qboolean VectorsEqual( const float *v1, const float *v2 );
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inline vec_t RoundInt (vec_t in)
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{
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return floor(in + 0.5f);
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}
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int Q_log2(int val);
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// Math routines done in optimized assembly math package routines
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void inline SinCos( float radians, float *sine, float *cosine )
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{
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#if defined( _X360 )
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XMScalarSinCos( sine, cosine, radians );
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#elif defined( PLATFORM_WINDOWS_PC32 )
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_asm
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{
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fld DWORD PTR [radians]
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fsincos
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mov edx, DWORD PTR [cosine]
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mov eax, DWORD PTR [sine]
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fstp DWORD PTR [edx]
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fstp DWORD PTR [eax]
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}
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#elif defined( PLATFORM_WINDOWS_PC64 )
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*sine = sin( radians );
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*cosine = cos( radians );
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#elif defined( POSIX )
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||
double __cosr, __sinr;
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__asm ("fsincos" : "=t" (__cosr), "=u" (__sinr) : "0" (radians));
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*sine = __sinr;
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*cosine = __cosr;
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#endif
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}
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|
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#define SIN_TABLE_SIZE 256
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||
#define FTOIBIAS 12582912.f
|
||
extern float SinCosTable[SIN_TABLE_SIZE];
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||
|
||
inline float TableCos( float theta )
|
||
{
|
||
union
|
||
{
|
||
int i;
|
||
float f;
|
||
} ftmp;
|
||
|
||
// ideally, the following should compile down to: theta * constant + constant, changing any of these constants from defines sometimes fubars this.
|
||
ftmp.f = theta * ( float )( SIN_TABLE_SIZE / ( 2.0f * M_PI ) ) + ( FTOIBIAS + ( SIN_TABLE_SIZE / 4 ) );
|
||
return SinCosTable[ ftmp.i & ( SIN_TABLE_SIZE - 1 ) ];
|
||
}
|
||
|
||
inline float TableSin( float theta )
|
||
{
|
||
union
|
||
{
|
||
int i;
|
||
float f;
|
||
} ftmp;
|
||
|
||
// ideally, the following should compile down to: theta * constant + constant
|
||
ftmp.f = theta * ( float )( SIN_TABLE_SIZE / ( 2.0f * M_PI ) ) + FTOIBIAS;
|
||
return SinCosTable[ ftmp.i & ( SIN_TABLE_SIZE - 1 ) ];
|
||
}
|
||
|
||
template<class T>
|
||
FORCEINLINE T Square( T const &a )
|
||
{
|
||
return a * a;
|
||
}
|
||
|
||
|
||
// return the smallest power of two >= x.
|
||
// returns 0 if x == 0 or x > 0x80000000 (ie numbers that would be negative if x was signed)
|
||
// NOTE: the old code took an int, and if you pass in an int of 0x80000000 casted to a uint,
|
||
// you'll get 0x80000000, which is correct for uints, instead of 0, which was correct for ints
|
||
FORCEINLINE uint SmallestPowerOfTwoGreaterOrEqual( uint x )
|
||
{
|
||
x -= 1;
|
||
x |= x >> 1;
|
||
x |= x >> 2;
|
||
x |= x >> 4;
|
||
x |= x >> 8;
|
||
x |= x >> 16;
|
||
return x + 1;
|
||
}
|
||
|
||
// return the largest power of two <= x. Will return 0 if passed 0
|
||
FORCEINLINE uint LargestPowerOfTwoLessThanOrEqual( uint x )
|
||
{
|
||
if ( x >= 0x80000000 )
|
||
return 0x80000000;
|
||
|
||
return SmallestPowerOfTwoGreaterOrEqual( x + 1 ) >> 1;
|
||
}
|
||
|
||
|
||
// Math routines for optimizing division
|
||
void FloorDivMod (double numer, double denom, int *quotient, int *rem);
|
||
int GreatestCommonDivisor (int i1, int i2);
|
||
|
||
// Test for FPU denormal mode
|
||
bool IsDenormal( const float &val );
|
||
|
||
// MOVEMENT INFO
|
||
enum
|
||
{
|
||
PITCH = 0, // up / down
|
||
YAW, // left / right
|
||
ROLL // fall over
|
||
};
|
||
|
||
void MatrixAngles( const matrix3x4_t & matrix, float *angles ); // !!!!
|
||
void MatrixVectors( const matrix3x4_t &matrix, Vector* pForward, Vector *pRight, Vector *pUp );
|
||
void VectorTransform (const float *in1, const matrix3x4_t & in2, float *out);
|
||
void VectorITransform (const float *in1, const matrix3x4_t & in2, float *out);
|
||
void VectorRotate( const float *in1, const matrix3x4_t & in2, float *out);
|
||
void VectorRotate( const Vector &in1, const QAngle &in2, Vector &out );
|
||
void VectorRotate( const Vector &in1, const Quaternion &in2, Vector &out );
|
||
void VectorIRotate( const float *in1, const matrix3x4_t & in2, float *out);
|
||
|
||
#ifndef VECTOR_NO_SLOW_OPERATIONS
|
||
|
||
QAngle TransformAnglesToLocalSpace( const QAngle &angles, const matrix3x4_t &parentMatrix );
|
||
QAngle TransformAnglesToWorldSpace( const QAngle &angles, const matrix3x4_t &parentMatrix );
|
||
|
||
#endif
|
||
|
||
void MatrixInitialize( matrix3x4_t &mat, const Vector &vecOrigin, const Vector &vecXAxis, const Vector &vecYAxis, const Vector &vecZAxis );
|
||
void MatrixCopy( const matrix3x4_t &in, matrix3x4_t &out );
|
||
void MatrixInvert( const matrix3x4_t &in, matrix3x4_t &out );
|
||
|
||
// Matrix equality test
|
||
bool MatricesAreEqual( const matrix3x4_t &src1, const matrix3x4_t &src2, float flTolerance = 1e-5 );
|
||
|
||
void MatrixGetColumn( const matrix3x4_t &in, int column, Vector &out );
|
||
void MatrixSetColumn( const Vector &in, int column, matrix3x4_t &out );
|
||
|
||
inline void MatrixGetTranslation( const matrix3x4_t &in, Vector &out )
|
||
{
|
||
MatrixGetColumn ( in, 3, out );
|
||
}
|
||
|
||
inline void MatrixSetTranslation( const Vector &in, matrix3x4_t &out )
|
||
{
|
||
MatrixSetColumn ( in, 3, out );
|
||
}
|
||
|
||
void MatrixScaleBy ( const float flScale, matrix3x4_t &out );
|
||
void MatrixScaleByZero ( matrix3x4_t &out );
|
||
|
||
//void DecomposeRotation( const matrix3x4_t &mat, float *out );
|
||
void ConcatRotations (const matrix3x4_t &in1, const matrix3x4_t &in2, matrix3x4_t &out);
|
||
void ConcatTransforms (const matrix3x4_t &in1, const matrix3x4_t &in2, matrix3x4_t &out);
|
||
|
||
// For identical interface w/ VMatrix
|
||
inline void MatrixMultiply ( const matrix3x4_t &in1, const matrix3x4_t &in2, matrix3x4_t &out )
|
||
{
|
||
ConcatTransforms( in1, in2, out );
|
||
}
|
||
|
||
void QuaternionSlerp( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt );
|
||
void QuaternionSlerpNoAlign( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt );
|
||
void QuaternionBlend( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt );
|
||
void QuaternionBlendNoAlign( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt );
|
||
void QuaternionIdentityBlend( const Quaternion &p, float t, Quaternion &qt );
|
||
float QuaternionAngleDiff( const Quaternion &p, const Quaternion &q );
|
||
void QuaternionScale( const Quaternion &p, float t, Quaternion &q );
|
||
void QuaternionAlign( const Quaternion &p, const Quaternion &q, Quaternion &qt );
|
||
float QuaternionDotProduct( const Quaternion &p, const Quaternion &q );
|
||
void QuaternionConjugate( const Quaternion &p, Quaternion &q );
|
||
void QuaternionInvert( const Quaternion &p, Quaternion &q );
|
||
float QuaternionNormalize( Quaternion &q );
|
||
void QuaternionAdd( const Quaternion &p, const Quaternion &q, Quaternion &qt );
|
||
void QuaternionMult( const Quaternion &p, const Quaternion &q, Quaternion &qt );
|
||
void QuaternionMatrix( const Quaternion &q, matrix3x4_t &matrix );
|
||
void QuaternionMatrix( const Quaternion &q, const Vector &pos, matrix3x4_t &matrix );
|
||
void QuaternionAngles( const Quaternion &q, QAngle &angles );
|
||
void AngleQuaternion( const QAngle& angles, Quaternion &qt );
|
||
void QuaternionAngles( const Quaternion &q, RadianEuler &angles );
|
||
void AngleQuaternion( RadianEuler const &angles, Quaternion &qt );
|
||
void QuaternionAxisAngle( const Quaternion &q, Vector &axis, float &angle );
|
||
void AxisAngleQuaternion( const Vector &axis, float angle, Quaternion &q );
|
||
void BasisToQuaternion( const Vector &vecForward, const Vector &vecRight, const Vector &vecUp, Quaternion &q );
|
||
void MatrixQuaternion( const matrix3x4_t &mat, Quaternion &q );
|
||
|
||
// A couple methods to find the dot product of a vector with a matrix row or column...
|
||
inline float MatrixRowDotProduct( const matrix3x4_t &in1, int row, const Vector& in2 )
|
||
{
|
||
Assert( (row >= 0) && (row < 3) );
|
||
return DotProduct( in1[row], in2.Base() );
|
||
}
|
||
|
||
inline float MatrixColumnDotProduct( const matrix3x4_t &in1, int col, const Vector& in2 )
|
||
{
|
||
Assert( (col >= 0) && (col < 4) );
|
||
return in1[0][col] * in2[0] + in1[1][col] * in2[1] + in1[2][col] * in2[2];
|
||
}
|
||
|
||
int __cdecl BoxOnPlaneSide (const float *emins, const float *emaxs, const cplane_t *plane);
|
||
|
||
inline float anglemod(float a)
|
||
{
|
||
a = (360.f/65536) * ((int)(a*(65536.f/360.0f)) & 65535);
|
||
return a;
|
||
}
|
||
|
||
// Remap a value in the range [A,B] to [C,D].
|
||
inline float RemapVal( float val, float A, float B, float C, float D)
|
||
{
|
||
if ( A == B )
|
||
return val >= B ? D : C;
|
||
return C + (D - C) * (val - A) / (B - A);
|
||
}
|
||
|
||
inline float RemapValClamped( float val, float A, float B, float C, float D)
|
||
{
|
||
if ( A == B )
|
||
return val >= B ? D : C;
|
||
float cVal = (val - A) / (B - A);
|
||
cVal = clamp( cVal, 0.0f, 1.0f );
|
||
|
||
return C + (D - C) * cVal;
|
||
}
|
||
|
||
// Returns A + (B-A)*flPercent.
|
||
// float Lerp( float flPercent, float A, float B );
|
||
template <class T>
|
||
FORCEINLINE T Lerp( float flPercent, T const &A, T const &B )
|
||
{
|
||
return A + (B - A) * flPercent;
|
||
}
|
||
|
||
FORCEINLINE float Sqr( float f )
|
||
{
|
||
return f*f;
|
||
}
|
||
|
||
// 5-argument floating point linear interpolation.
|
||
// FLerp(f1,f2,i1,i2,x)=
|
||
// f1 at x=i1
|
||
// f2 at x=i2
|
||
// smooth lerp between f1 and f2 at x>i1 and x<i2
|
||
// extrapolation for x<i1 or x>i2
|
||
//
|
||
// If you know a function f(x)'s value (f1) at position i1, and its value (f2) at position i2,
|
||
// the function can be linearly interpolated with FLerp(f1,f2,i1,i2,x)
|
||
// i2=i1 will cause a divide by zero.
|
||
static inline float FLerp(float f1, float f2, float i1, float i2, float x)
|
||
{
|
||
return f1+(f2-f1)*(x-i1)/(i2-i1);
|
||
}
|
||
|
||
|
||
#ifndef VECTOR_NO_SLOW_OPERATIONS
|
||
|
||
// YWB: Specialization for interpolating euler angles via quaternions...
|
||
template<> FORCEINLINE QAngle Lerp<QAngle>( float flPercent, const QAngle& q1, const QAngle& q2 )
|
||
{
|
||
// Avoid precision errors
|
||
if ( q1 == q2 )
|
||
return q1;
|
||
|
||
Quaternion src, dest;
|
||
|
||
// Convert to quaternions
|
||
AngleQuaternion( q1, src );
|
||
AngleQuaternion( q2, dest );
|
||
|
||
Quaternion result;
|
||
|
||
// Slerp
|
||
QuaternionSlerp( src, dest, flPercent, result );
|
||
|
||
// Convert to euler
|
||
QAngle output;
|
||
QuaternionAngles( result, output );
|
||
return output;
|
||
}
|
||
|
||
#else
|
||
|
||
#pragma error
|
||
|
||
// NOTE NOTE: I haven't tested this!! It may not work! Check out interpolatedvar.cpp in the client dll to try it
|
||
template<> FORCEINLINE QAngleByValue Lerp<QAngleByValue>( float flPercent, const QAngleByValue& q1, const QAngleByValue& q2 )
|
||
{
|
||
// Avoid precision errors
|
||
if ( q1 == q2 )
|
||
return q1;
|
||
|
||
Quaternion src, dest;
|
||
|
||
// Convert to quaternions
|
||
AngleQuaternion( q1, src );
|
||
AngleQuaternion( q2, dest );
|
||
|
||
Quaternion result;
|
||
|
||
// Slerp
|
||
QuaternionSlerp( src, dest, flPercent, result );
|
||
|
||
// Convert to euler
|
||
QAngleByValue output;
|
||
QuaternionAngles( result, output );
|
||
return output;
|
||
}
|
||
|
||
#endif // VECTOR_NO_SLOW_OPERATIONS
|
||
|
||
|
||
/// Same as swap(), but won't cause problems with std::swap
|
||
template <class T>
|
||
FORCEINLINE void V_swap( T& x, T& y )
|
||
{
|
||
T temp = x;
|
||
x = y;
|
||
y = temp;
|
||
}
|
||
|
||
template <class T> FORCEINLINE T AVG(T a, T b)
|
||
{
|
||
return (a+b)/2;
|
||
}
|
||
|
||
// number of elements in an array of static size
|
||
#define NELEMS(x) ARRAYSIZE(x)
|
||
|
||
// XYZ macro, for printf type functions - ex printf("%f %f %f",XYZ(myvector));
|
||
#define XYZ(v) (v).x,(v).y,(v).z
|
||
|
||
|
||
inline float Sign( float x )
|
||
{
|
||
return (x <0.0f) ? -1.0f : 1.0f;
|
||
}
|
||
|
||
//
|
||
// Clamps the input integer to the given array bounds.
|
||
// Equivalent to the following, but without using any branches:
|
||
//
|
||
// if( n < 0 ) return 0;
|
||
// else if ( n > maxindex ) return maxindex;
|
||
// else return n;
|
||
//
|
||
// This is not always a clear performance win, but when you have situations where a clamped
|
||
// value is thrashing against a boundary this is a big win. (ie, valid, invalid, valid, invalid, ...)
|
||
//
|
||
// Note: This code has been run against all possible integers.
|
||
//
|
||
inline int ClampArrayBounds( int n, unsigned maxindex )
|
||
{
|
||
// mask is 0 if less than 4096, 0xFFFFFFFF if greater than
|
||
unsigned int inrangemask = 0xFFFFFFFF + (((unsigned) n) > maxindex );
|
||
unsigned int lessthan0mask = 0xFFFFFFFF + ( n >= 0 );
|
||
|
||
// If the result was valid, set the result, (otherwise sets zero)
|
||
int result = (inrangemask & n);
|
||
|
||
// if the result was out of range or zero.
|
||
result |= ((~inrangemask) & (~lessthan0mask)) & maxindex;
|
||
|
||
return result;
|
||
}
|
||
|
||
|
||
#define BOX_ON_PLANE_SIDE(emins, emaxs, p) \
|
||
(((p)->type < 3)? \
|
||
( \
|
||
((p)->dist <= (emins)[(p)->type])? \
|
||
1 \
|
||
: \
|
||
( \
|
||
((p)->dist >= (emaxs)[(p)->type])?\
|
||
2 \
|
||
: \
|
||
3 \
|
||
) \
|
||
) \
|
||
: \
|
||
BoxOnPlaneSide( (emins), (emaxs), (p)))
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// FIXME: Vector versions.... the float versions will go away hopefully soon!
|
||
//-----------------------------------------------------------------------------
|
||
|
||
void AngleVectors (const QAngle& angles, Vector *forward);
|
||
void AngleVectors (const QAngle& angles, Vector *forward, Vector *right, Vector *up);
|
||
void AngleVectorsTranspose (const QAngle& angles, Vector *forward, Vector *right, Vector *up);
|
||
void AngleMatrix (const QAngle &angles, matrix3x4_t &mat );
|
||
void AngleMatrix( const QAngle &angles, const Vector &position, matrix3x4_t &mat );
|
||
void AngleMatrix (const RadianEuler &angles, matrix3x4_t &mat );
|
||
void AngleMatrix( RadianEuler const &angles, const Vector &position, matrix3x4_t &mat );
|
||
void AngleIMatrix (const QAngle &angles, matrix3x4_t &mat );
|
||
void AngleIMatrix (const QAngle &angles, const Vector &position, matrix3x4_t &mat );
|
||
void AngleIMatrix (const RadianEuler &angles, matrix3x4_t &mat );
|
||
void VectorAngles( const Vector &forward, QAngle &angles );
|
||
void VectorAngles( const Vector &forward, const Vector &pseudoup, QAngle &angles );
|
||
void VectorMatrix( const Vector &forward, matrix3x4_t &mat );
|
||
void VectorVectors( const Vector &forward, Vector &right, Vector &up );
|
||
void SetIdentityMatrix( matrix3x4_t &mat );
|
||
void SetScaleMatrix( float x, float y, float z, matrix3x4_t &dst );
|
||
void MatrixBuildRotationAboutAxis( const Vector &vAxisOfRot, float angleDegrees, matrix3x4_t &dst );
|
||
|
||
inline void SetScaleMatrix( float flScale, matrix3x4_t &dst )
|
||
{
|
||
SetScaleMatrix( flScale, flScale, flScale, dst );
|
||
}
|
||
|
||
inline void SetScaleMatrix( const Vector& scale, matrix3x4_t &dst )
|
||
{
|
||
SetScaleMatrix( scale.x, scale.y, scale.z, dst );
|
||
}
|
||
|
||
// Computes the inverse transpose
|
||
void MatrixTranspose( matrix3x4_t& mat );
|
||
void MatrixTranspose( const matrix3x4_t& src, matrix3x4_t& dst );
|
||
void MatrixInverseTranspose( const matrix3x4_t& src, matrix3x4_t& dst );
|
||
|
||
inline void PositionMatrix( const Vector &position, matrix3x4_t &mat )
|
||
{
|
||
MatrixSetColumn( position, 3, mat );
|
||
}
|
||
|
||
inline void MatrixPosition( const matrix3x4_t &matrix, Vector &position )
|
||
{
|
||
MatrixGetColumn( matrix, 3, position );
|
||
}
|
||
|
||
inline void VectorRotate( const Vector& in1, const matrix3x4_t &in2, Vector &out)
|
||
{
|
||
VectorRotate( &in1.x, in2, &out.x );
|
||
}
|
||
|
||
inline void VectorIRotate( const Vector& in1, const matrix3x4_t &in2, Vector &out)
|
||
{
|
||
VectorIRotate( &in1.x, in2, &out.x );
|
||
}
|
||
|
||
inline void MatrixAngles( const matrix3x4_t &matrix, QAngle &angles )
|
||
{
|
||
MatrixAngles( matrix, &angles.x );
|
||
}
|
||
|
||
inline void MatrixAngles( const matrix3x4_t &matrix, QAngle &angles, Vector &position )
|
||
{
|
||
MatrixAngles( matrix, angles );
|
||
MatrixPosition( matrix, position );
|
||
}
|
||
|
||
inline void MatrixAngles( const matrix3x4_t &matrix, RadianEuler &angles )
|
||
{
|
||
MatrixAngles( matrix, &angles.x );
|
||
|
||
angles.Init( DEG2RAD( angles.z ), DEG2RAD( angles.x ), DEG2RAD( angles.y ) );
|
||
}
|
||
|
||
void MatrixAngles( const matrix3x4_t &mat, RadianEuler &angles, Vector &position );
|
||
|
||
void MatrixAngles( const matrix3x4_t &mat, Quaternion &q, Vector &position );
|
||
|
||
inline int VectorCompare (const Vector& v1, const Vector& v2)
|
||
{
|
||
return v1 == v2;
|
||
}
|
||
|
||
inline void VectorTransform (const Vector& in1, const matrix3x4_t &in2, Vector &out)
|
||
{
|
||
VectorTransform( &in1.x, in2, &out.x );
|
||
}
|
||
|
||
inline void VectorITransform (const Vector& in1, const matrix3x4_t &in2, Vector &out)
|
||
{
|
||
VectorITransform( &in1.x, in2, &out.x );
|
||
}
|
||
|
||
/*
|
||
inline void DecomposeRotation( const matrix3x4_t &mat, Vector &out )
|
||
{
|
||
DecomposeRotation( mat, &out.x );
|
||
}
|
||
*/
|
||
|
||
inline int BoxOnPlaneSide (const Vector& emins, const Vector& emaxs, const cplane_t *plane )
|
||
{
|
||
return BoxOnPlaneSide( &emins.x, &emaxs.x, plane );
|
||
}
|
||
|
||
inline void VectorFill(Vector& a, float b)
|
||
{
|
||
a[0]=a[1]=a[2]=b;
|
||
}
|
||
|
||
inline void VectorNegate(Vector& a)
|
||
{
|
||
a[0] = -a[0];
|
||
a[1] = -a[1];
|
||
a[2] = -a[2];
|
||
}
|
||
|
||
inline vec_t VectorAvg(Vector& a)
|
||
{
|
||
return ( a[0] + a[1] + a[2] ) / 3;
|
||
}
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// Box/plane test (slow version)
|
||
//-----------------------------------------------------------------------------
|
||
inline int FASTCALL BoxOnPlaneSide2 (const Vector& emins, const Vector& emaxs, const cplane_t *p, float tolerance = 0.f )
|
||
{
|
||
Vector corners[2];
|
||
|
||
if (p->normal[0] < 0)
|
||
{
|
||
corners[0][0] = emins[0];
|
||
corners[1][0] = emaxs[0];
|
||
}
|
||
else
|
||
{
|
||
corners[1][0] = emins[0];
|
||
corners[0][0] = emaxs[0];
|
||
}
|
||
|
||
if (p->normal[1] < 0)
|
||
{
|
||
corners[0][1] = emins[1];
|
||
corners[1][1] = emaxs[1];
|
||
}
|
||
else
|
||
{
|
||
corners[1][1] = emins[1];
|
||
corners[0][1] = emaxs[1];
|
||
}
|
||
|
||
if (p->normal[2] < 0)
|
||
{
|
||
corners[0][2] = emins[2];
|
||
corners[1][2] = emaxs[2];
|
||
}
|
||
else
|
||
{
|
||
corners[1][2] = emins[2];
|
||
corners[0][2] = emaxs[2];
|
||
}
|
||
|
||
int sides = 0;
|
||
|
||
float dist1 = DotProduct (p->normal, corners[0]) - p->dist;
|
||
if (dist1 >= tolerance)
|
||
sides = 1;
|
||
|
||
float dist2 = DotProduct (p->normal, corners[1]) - p->dist;
|
||
if (dist2 < -tolerance)
|
||
sides |= 2;
|
||
|
||
return sides;
|
||
}
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// Helpers for bounding box construction
|
||
//-----------------------------------------------------------------------------
|
||
|
||
void ClearBounds (Vector& mins, Vector& maxs);
|
||
void AddPointToBounds (const Vector& v, Vector& mins, Vector& maxs);
|
||
|
||
//
|
||
// COLORSPACE/GAMMA CONVERSION STUFF
|
||
//
|
||
void BuildGammaTable( float gamma, float texGamma, float brightness, int overbright );
|
||
|
||
// convert texture to linear 0..1 value
|
||
inline float TexLightToLinear( int c, int exponent )
|
||
{
|
||
extern float power2_n[256];
|
||
Assert( exponent >= -128 && exponent <= 127 );
|
||
return ( float )c * power2_n[exponent+128];
|
||
}
|
||
|
||
|
||
// convert texture to linear 0..1 value
|
||
int LinearToTexture( float f );
|
||
// converts 0..1 linear value to screen gamma (0..255)
|
||
int LinearToScreenGamma( float f );
|
||
float TextureToLinear( int c );
|
||
|
||
// compressed color format
|
||
struct ColorRGBExp32
|
||
{
|
||
byte r, g, b;
|
||
signed char exponent;
|
||
};
|
||
|
||
void ColorRGBExp32ToVector( const ColorRGBExp32& in, Vector& out );
|
||
void VectorToColorRGBExp32( const Vector& v, ColorRGBExp32 &c );
|
||
|
||
// solve for "x" where "a x^2 + b x + c = 0", return true if solution exists
|
||
bool SolveQuadratic( float a, float b, float c, float &root1, float &root2 );
|
||
|
||
// solves for "a, b, c" where "a x^2 + b x + c = y", return true if solution exists
|
||
bool SolveInverseQuadratic( float x1, float y1, float x2, float y2, float x3, float y3, float &a, float &b, float &c );
|
||
|
||
// solves for a,b,c specified as above, except that it always creates a monotonically increasing or
|
||
// decreasing curve if the data is monotonically increasing or decreasing. In order to enforce the
|
||
// monoticity condition, it is possible that the resulting quadratic will only approximate the data
|
||
// instead of interpolating it. This code is not especially fast.
|
||
bool SolveInverseQuadraticMonotonic( float x1, float y1, float x2, float y2,
|
||
float x3, float y3, float &a, float &b, float &c );
|
||
|
||
|
||
|
||
|
||
// solves for "a, b, c" where "1/(a x^2 + b x + c ) = y", return true if solution exists
|
||
bool SolveInverseReciprocalQuadratic( float x1, float y1, float x2, float y2, float x3, float y3, float &a, float &b, float &c );
|
||
|
||
// rotate a vector around the Z axis (YAW)
|
||
void VectorYawRotate( const Vector& in, float flYaw, Vector &out);
|
||
|
||
|
||
// Bias takes an X value between 0 and 1 and returns another value between 0 and 1
|
||
// The curve is biased towards 0 or 1 based on biasAmt, which is between 0 and 1.
|
||
// Lower values of biasAmt bias the curve towards 0 and higher values bias it towards 1.
|
||
//
|
||
// For example, with biasAmt = 0.2, the curve looks like this:
|
||
//
|
||
// 1
|
||
// | *
|
||
// | *
|
||
// | *
|
||
// | **
|
||
// | **
|
||
// | ****
|
||
// |*********
|
||
// |___________________
|
||
// 0 1
|
||
//
|
||
//
|
||
// With biasAmt = 0.8, the curve looks like this:
|
||
//
|
||
// 1
|
||
// | **************
|
||
// | **
|
||
// | *
|
||
// | *
|
||
// |*
|
||
// |*
|
||
// |*
|
||
// |___________________
|
||
// 0 1
|
||
//
|
||
// With a biasAmt of 0.5, Bias returns X.
|
||
float Bias( float x, float biasAmt );
|
||
|
||
|
||
// Gain is similar to Bias, but biasAmt biases towards or away from 0.5.
|
||
// Lower bias values bias towards 0.5 and higher bias values bias away from it.
|
||
//
|
||
// For example, with biasAmt = 0.2, the curve looks like this:
|
||
//
|
||
// 1
|
||
// | *
|
||
// | *
|
||
// | **
|
||
// | ***************
|
||
// | **
|
||
// | *
|
||
// |*
|
||
// |___________________
|
||
// 0 1
|
||
//
|
||
//
|
||
// With biasAmt = 0.8, the curve looks like this:
|
||
//
|
||
// 1
|
||
// | *****
|
||
// | ***
|
||
// | *
|
||
// | *
|
||
// | *
|
||
// | ***
|
||
// |*****
|
||
// |___________________
|
||
// 0 1
|
||
float Gain( float x, float biasAmt );
|
||
|
||
|
||
// SmoothCurve maps a 0-1 value into another 0-1 value based on a cosine wave
|
||
// where the derivatives of the function at 0 and 1 (and 0.5) are 0. This is useful for
|
||
// any fadein/fadeout effect where it should start and end smoothly.
|
||
//
|
||
// The curve looks like this:
|
||
//
|
||
// 1
|
||
// | **
|
||
// | * *
|
||
// | * *
|
||
// | * *
|
||
// | * *
|
||
// | ** **
|
||
// |*** ***
|
||
// |___________________
|
||
// 0 1
|
||
//
|
||
float SmoothCurve( float x );
|
||
|
||
|
||
// This works like SmoothCurve, with two changes:
|
||
//
|
||
// 1. Instead of the curve peaking at 0.5, it will peak at flPeakPos.
|
||
// (So if you specify flPeakPos=0.2, then the peak will slide to the left).
|
||
//
|
||
// 2. flPeakSharpness is a 0-1 value controlling the sharpness of the peak.
|
||
// Low values blunt the peak and high values sharpen the peak.
|
||
float SmoothCurve_Tweak( float x, float flPeakPos=0.5, float flPeakSharpness=0.5 );
|
||
|
||
|
||
//float ExponentialDecay( float halflife, float dt );
|
||
//float ExponentialDecay( float decayTo, float decayTime, float dt );
|
||
|
||
// halflife is time for value to reach 50%
|
||
inline float ExponentialDecay( float halflife, float dt )
|
||
{
|
||
// log(0.5) == -0.69314718055994530941723212145818
|
||
return expf( -0.69314718f / halflife * dt);
|
||
}
|
||
|
||
// decayTo is factor the value should decay to in decayTime
|
||
inline float ExponentialDecay( float decayTo, float decayTime, float dt )
|
||
{
|
||
return expf( logf( decayTo ) / decayTime * dt);
|
||
}
|
||
|
||
// Get the integrated distanced traveled
|
||
// decayTo is factor the value should decay to in decayTime
|
||
// dt is the time relative to the last velocity update
|
||
inline float ExponentialDecayIntegral( float decayTo, float decayTime, float dt )
|
||
{
|
||
return (powf( decayTo, dt / decayTime) * decayTime - decayTime) / logf( decayTo );
|
||
}
|
||
|
||
// hermite basis function for smooth interpolation
|
||
// Similar to Gain() above, but very cheap to call
|
||
// value should be between 0 & 1 inclusive
|
||
inline float SimpleSpline( float value )
|
||
{
|
||
float valueSquared = value * value;
|
||
|
||
// Nice little ease-in, ease-out spline-like curve
|
||
return (3 * valueSquared - 2 * valueSquared * value);
|
||
}
|
||
|
||
// remaps a value in [startInterval, startInterval+rangeInterval] from linear to
|
||
// spline using SimpleSpline
|
||
inline float SimpleSplineRemapVal( float val, float A, float B, float C, float D)
|
||
{
|
||
if ( A == B )
|
||
return val >= B ? D : C;
|
||
float cVal = (val - A) / (B - A);
|
||
return C + (D - C) * SimpleSpline( cVal );
|
||
}
|
||
|
||
// remaps a value in [startInterval, startInterval+rangeInterval] from linear to
|
||
// spline using SimpleSpline
|
||
inline float SimpleSplineRemapValClamped( float val, float A, float B, float C, float D )
|
||
{
|
||
if ( A == B )
|
||
return val >= B ? D : C;
|
||
float cVal = (val - A) / (B - A);
|
||
cVal = clamp( cVal, 0.0f, 1.0f );
|
||
return C + (D - C) * SimpleSpline( cVal );
|
||
}
|
||
|
||
FORCEINLINE int RoundFloatToInt(float f)
|
||
{
|
||
#if defined(__i386__) || defined(_M_IX86) || defined( PLATFORM_WINDOWS_PC64 ) || defined(__x86_64__)
|
||
return _mm_cvtss_si32(_mm_load_ss(&f));
|
||
#elif defined( _X360 )
|
||
#ifdef Assert
|
||
Assert( IsFPUControlWordSet() );
|
||
#endif
|
||
union
|
||
{
|
||
double flResult;
|
||
int pResult[2];
|
||
};
|
||
flResult = __fctiw( f );
|
||
return pResult[1];
|
||
#else
|
||
#error Unknown architecture
|
||
#endif
|
||
}
|
||
|
||
FORCEINLINE unsigned char RoundFloatToByte(float f)
|
||
{
|
||
int nResult = RoundFloatToInt(f);
|
||
#ifdef Assert
|
||
Assert( (nResult & ~0xFF) == 0 );
|
||
#endif
|
||
return (unsigned char) nResult;
|
||
}
|
||
|
||
FORCEINLINE unsigned long RoundFloatToUnsignedLong(float f)
|
||
{
|
||
#if defined( _X360 )
|
||
#ifdef Assert
|
||
Assert( IsFPUControlWordSet() );
|
||
#endif
|
||
union
|
||
{
|
||
double flResult;
|
||
int pIntResult[2];
|
||
unsigned long pResult[2];
|
||
};
|
||
flResult = __fctiw( f );
|
||
Assert( pIntResult[1] >= 0 );
|
||
return pResult[1];
|
||
#else // !X360
|
||
|
||
#if defined( PLATFORM_WINDOWS_PC64 )
|
||
uint nRet = ( uint ) f;
|
||
if ( nRet & 1 )
|
||
{
|
||
if ( ( f - floor( f ) >= 0.5 ) )
|
||
{
|
||
nRet++;
|
||
}
|
||
}
|
||
else
|
||
{
|
||
if ( ( f - floor( f ) > 0.5 ) )
|
||
{
|
||
nRet++;
|
||
}
|
||
}
|
||
return nRet;
|
||
#else // PLATFORM_WINDOWS_PC64
|
||
unsigned char nResult[8];
|
||
|
||
#if defined( _WIN32 )
|
||
__asm
|
||
{
|
||
fld f
|
||
fistp qword ptr nResult
|
||
}
|
||
#elif POSIX
|
||
__asm __volatile__ (
|
||
"fistpl %0;": "=m" (nResult): "t" (f) : "st"
|
||
);
|
||
#endif
|
||
|
||
return *((unsigned long*)nResult);
|
||
#endif // PLATFORM_WINDOWS_PC64
|
||
#endif // !X360
|
||
}
|
||
|
||
FORCEINLINE bool IsIntegralValue( float flValue, float flTolerance = 0.001f )
|
||
{
|
||
return fabs( RoundFloatToInt( flValue ) - flValue ) < flTolerance;
|
||
}
|
||
|
||
// Fast, accurate ftol:
|
||
FORCEINLINE int Float2Int( float a )
|
||
{
|
||
#if defined( _X360 )
|
||
union
|
||
{
|
||
double flResult;
|
||
int pResult[2];
|
||
};
|
||
flResult = __fctiwz( a );
|
||
return pResult[1];
|
||
#else // !X360
|
||
// Rely on compiler to generate CVTTSS2SI on x86
|
||
return (int) a;
|
||
#endif
|
||
}
|
||
|
||
// Over 15x faster than: (int)floor(value)
|
||
inline int Floor2Int( float a )
|
||
{
|
||
int RetVal;
|
||
#if defined( __i386__ )
|
||
// Convert to int and back, compare, subtract one if too big
|
||
__m128 a128 = _mm_set_ss(a);
|
||
RetVal = _mm_cvtss_si32(a128);
|
||
__m128 rounded128 = _mm_cvt_si2ss(_mm_setzero_ps(), RetVal);
|
||
RetVal -= _mm_comigt_ss( rounded128, a128 );
|
||
#else
|
||
RetVal = static_cast<int>( floor(a) );
|
||
#endif
|
||
return RetVal;
|
||
}
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// Fast color conversion from float to unsigned char
|
||
//-----------------------------------------------------------------------------
|
||
FORCEINLINE unsigned int FastFToC( float c )
|
||
{
|
||
#if defined( __i386__ )
|
||
// IEEE float bit manipulation works for values between [0, 1<<23)
|
||
union { float f; int i; } convert = { c*255.0f + (float)(1<<23) };
|
||
return convert.i & 255;
|
||
#else
|
||
// consoles CPUs suffer from load-hit-store penalty
|
||
return Float2Int( c * 255.0f );
|
||
#endif
|
||
}
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// Fast conversion from float to integer with magnitude less than 2**22
|
||
//-----------------------------------------------------------------------------
|
||
FORCEINLINE int FastFloatToSmallInt( float c )
|
||
{
|
||
#if defined( __i386__ )
|
||
// IEEE float bit manipulation works for values between [-1<<22, 1<<22)
|
||
union { float f; int i; } convert = { c + (float)(3<<22) };
|
||
return (convert.i & ((1<<23)-1)) - (1<<22);
|
||
#else
|
||
// consoles CPUs suffer from load-hit-store penalty
|
||
return Float2Int( c );
|
||
#endif
|
||
}
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// Purpose: Bound input float to .001 (millisecond) boundary
|
||
// Input : in -
|
||
// Output : inline float
|
||
//-----------------------------------------------------------------------------
|
||
inline float ClampToMsec( float in )
|
||
{
|
||
int msec = Floor2Int( in * 1000.0f + 0.5f );
|
||
return 0.001f * msec;
|
||
}
|
||
|
||
// Over 15x faster than: (int)ceil(value)
|
||
inline int Ceil2Int( float a )
|
||
{
|
||
int RetVal;
|
||
#if defined( __i386__ )
|
||
// Convert to int and back, compare, add one if too small
|
||
__m128 a128 = _mm_load_ss(&a);
|
||
RetVal = _mm_cvtss_si32(a128);
|
||
__m128 rounded128 = _mm_cvt_si2ss(_mm_setzero_ps(), RetVal);
|
||
RetVal += _mm_comilt_ss( rounded128, a128 );
|
||
#else
|
||
RetVal = static_cast<int>( ceil(a) );
|
||
#endif
|
||
return RetVal;
|
||
}
|
||
|
||
|
||
// Regular signed area of triangle
|
||
#define TriArea2D( A, B, C ) \
|
||
( 0.5f * ( ( B.x - A.x ) * ( C.y - A.y ) - ( B.y - A.y ) * ( C.x - A.x ) ) )
|
||
|
||
// This version doesn't premultiply by 0.5f, so it's the area of the rectangle instead
|
||
#define TriArea2DTimesTwo( A, B, C ) \
|
||
( ( ( B.x - A.x ) * ( C.y - A.y ) - ( B.y - A.y ) * ( C.x - A.x ) ) )
|
||
|
||
|
||
// Get the barycentric coordinates of "pt" in triangle [A,B,C].
|
||
inline void GetBarycentricCoords2D(
|
||
Vector2D const &A,
|
||
Vector2D const &B,
|
||
Vector2D const &C,
|
||
Vector2D const &pt,
|
||
float bcCoords[3] )
|
||
{
|
||
// Note, because to top and bottom are both x2, the issue washes out in the composite
|
||
float invTriArea = 1.0f / TriArea2DTimesTwo( A, B, C );
|
||
|
||
// NOTE: We assume here that the lightmap coordinate vertices go counterclockwise.
|
||
// If not, TriArea2D() is negated so this works out right.
|
||
bcCoords[0] = TriArea2DTimesTwo( B, C, pt ) * invTriArea;
|
||
bcCoords[1] = TriArea2DTimesTwo( C, A, pt ) * invTriArea;
|
||
bcCoords[2] = TriArea2DTimesTwo( A, B, pt ) * invTriArea;
|
||
}
|
||
|
||
|
||
// Return true of the sphere might touch the box (the sphere is actually treated
|
||
// like a box itself, so this may return true if the sphere's bounding box touches
|
||
// a corner of the box but the sphere itself doesn't).
|
||
inline bool QuickBoxSphereTest(
|
||
const Vector& vOrigin,
|
||
float flRadius,
|
||
const Vector& bbMin,
|
||
const Vector& bbMax )
|
||
{
|
||
return vOrigin.x - flRadius < bbMax.x && vOrigin.x + flRadius > bbMin.x &&
|
||
vOrigin.y - flRadius < bbMax.y && vOrigin.y + flRadius > bbMin.y &&
|
||
vOrigin.z - flRadius < bbMax.z && vOrigin.z + flRadius > bbMin.z;
|
||
}
|
||
|
||
|
||
// Return true of the boxes intersect (but not if they just touch).
|
||
inline bool QuickBoxIntersectTest(
|
||
const Vector& vBox1Min,
|
||
const Vector& vBox1Max,
|
||
const Vector& vBox2Min,
|
||
const Vector& vBox2Max )
|
||
{
|
||
return
|
||
vBox1Min.x < vBox2Max.x && vBox1Max.x > vBox2Min.x &&
|
||
vBox1Min.y < vBox2Max.y && vBox1Max.y > vBox2Min.y &&
|
||
vBox1Min.z < vBox2Max.z && vBox1Max.z > vBox2Min.z;
|
||
}
|
||
|
||
|
||
extern float GammaToLinearFullRange( float gamma );
|
||
extern float LinearToGammaFullRange( float linear );
|
||
extern float GammaToLinear( float gamma );
|
||
extern float LinearToGamma( float linear );
|
||
|
||
extern float SrgbGammaToLinear( float flSrgbGammaValue );
|
||
extern float SrgbLinearToGamma( float flLinearValue );
|
||
extern float X360GammaToLinear( float fl360GammaValue );
|
||
extern float X360LinearToGamma( float flLinearValue );
|
||
extern float SrgbGammaTo360Gamma( float flSrgbGammaValue );
|
||
|
||
// linear (0..4) to screen corrected vertex space (0..1?)
|
||
FORCEINLINE float LinearToVertexLight( float f )
|
||
{
|
||
extern float lineartovertex[4096];
|
||
|
||
// Gotta clamp before the multiply; could overflow...
|
||
// assume 0..4 range
|
||
int i = RoundFloatToInt( f * 1024.f );
|
||
|
||
// Presumably the comman case will be not to clamp, so check that first:
|
||
if( (unsigned)i > 4095 )
|
||
{
|
||
if ( i < 0 )
|
||
i = 0; // Compare to zero instead of 4095 to save 4 bytes in the instruction stream
|
||
else
|
||
i = 4095;
|
||
}
|
||
|
||
return lineartovertex[i];
|
||
}
|
||
|
||
|
||
FORCEINLINE unsigned char LinearToLightmap( float f )
|
||
{
|
||
extern unsigned char lineartolightmap[4096];
|
||
|
||
// Gotta clamp before the multiply; could overflow...
|
||
int i = RoundFloatToInt( f * 1024.f ); // assume 0..4 range
|
||
|
||
// Presumably the comman case will be not to clamp, so check that first:
|
||
if ( (unsigned)i > 4095 )
|
||
{
|
||
if ( i < 0 )
|
||
i = 0; // Compare to zero instead of 4095 to save 4 bytes in the instruction stream
|
||
else
|
||
i = 4095;
|
||
}
|
||
|
||
return lineartolightmap[i];
|
||
}
|
||
|
||
FORCEINLINE void ColorClamp( Vector& color )
|
||
{
|
||
float maxc = max( color.x, max( color.y, color.z ) );
|
||
if ( maxc > 1.0f )
|
||
{
|
||
float ooMax = 1.0f / maxc;
|
||
color.x *= ooMax;
|
||
color.y *= ooMax;
|
||
color.z *= ooMax;
|
||
}
|
||
|
||
if ( color[0] < 0.f ) color[0] = 0.f;
|
||
if ( color[1] < 0.f ) color[1] = 0.f;
|
||
if ( color[2] < 0.f ) color[2] = 0.f;
|
||
}
|
||
|
||
inline void ColorClampTruncate( Vector& color )
|
||
{
|
||
if (color[0] > 1.0f) color[0] = 1.0f; else if (color[0] < 0.0f) color[0] = 0.0f;
|
||
if (color[1] > 1.0f) color[1] = 1.0f; else if (color[1] < 0.0f) color[1] = 0.0f;
|
||
if (color[2] > 1.0f) color[2] = 1.0f; else if (color[2] < 0.0f) color[2] = 0.0f;
|
||
}
|
||
|
||
// Interpolate a Catmull-Rom spline.
|
||
// t is a [0,1] value and interpolates a curve between p2 and p3.
|
||
void Catmull_Rom_Spline(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector &output );
|
||
|
||
// Interpolate a Catmull-Rom spline.
|
||
// Returns the tangent of the point at t of the spline
|
||
void Catmull_Rom_Spline_Tangent(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector &output );
|
||
|
||
// area under the curve [0..t]
|
||
void Catmull_Rom_Spline_Integral(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector& output );
|
||
|
||
// area under the curve [0..1]
|
||
void Catmull_Rom_Spline_Integral(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
Vector& output );
|
||
|
||
// Interpolate a Catmull-Rom spline.
|
||
// Normalize p2->p1 and p3->p4 to be the same length as p2->p3
|
||
void Catmull_Rom_Spline_Normalize(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector &output );
|
||
|
||
// area under the curve [0..t]
|
||
// Normalize p2->p1 and p3->p4 to be the same length as p2->p3
|
||
void Catmull_Rom_Spline_Integral_Normalize(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector& output );
|
||
|
||
// Interpolate a Catmull-Rom spline.
|
||
// Normalize p2.x->p1.x and p3.x->p4.x to be the same length as p2.x->p3.x
|
||
void Catmull_Rom_Spline_NormalizeX(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector &output );
|
||
|
||
// area under the curve [0..t]
|
||
void Catmull_Rom_Spline_NormalizeX(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector& output );
|
||
|
||
// Interpolate a Hermite spline.
|
||
// t is a [0,1] value and interpolates a curve between p1 and p2 with the deltas d1 and d2.
|
||
void Hermite_Spline(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &d1,
|
||
const Vector &d2,
|
||
float t,
|
||
Vector& output );
|
||
|
||
float Hermite_Spline(
|
||
float p1,
|
||
float p2,
|
||
float d1,
|
||
float d2,
|
||
float t );
|
||
|
||
// t is a [0,1] value and interpolates a curve between p1 and p2 with the slopes p0->p1 and p1->p2
|
||
void Hermite_Spline(
|
||
const Vector &p0,
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
float t,
|
||
Vector& output );
|
||
|
||
float Hermite_Spline(
|
||
float p0,
|
||
float p1,
|
||
float p2,
|
||
float t );
|
||
|
||
|
||
void Hermite_SplineBasis( float t, float basis[] );
|
||
|
||
void Hermite_Spline(
|
||
const Quaternion &q0,
|
||
const Quaternion &q1,
|
||
const Quaternion &q2,
|
||
float t,
|
||
Quaternion &output );
|
||
|
||
|
||
// See http://en.wikipedia.org/wiki/Kochanek-Bartels_curves
|
||
//
|
||
// Tension: -1 = Round -> 1 = Tight
|
||
// Bias: -1 = Pre-shoot (bias left) -> 1 = Post-shoot (bias right)
|
||
// Continuity: -1 = Box corners -> 1 = Inverted corners
|
||
//
|
||
// If T=B=C=0 it's the same matrix as Catmull-Rom.
|
||
// If T=1 & B=C=0 it's the same as Cubic.
|
||
// If T=B=0 & C=-1 it's just linear interpolation
|
||
//
|
||
// See http://news.povray.org/povray.binaries.tutorials/attachment/%3CXns91B880592482seed7@povray.org%3E/Splines.bas.txt
|
||
// for example code and descriptions of various spline types...
|
||
//
|
||
void Kochanek_Bartels_Spline(
|
||
float tension,
|
||
float bias,
|
||
float continuity,
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector& output );
|
||
|
||
void Kochanek_Bartels_Spline_NormalizeX(
|
||
float tension,
|
||
float bias,
|
||
float continuity,
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector& output );
|
||
|
||
// See link at Kochanek_Bartels_Spline for info on the basis matrix used
|
||
void Cubic_Spline(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector& output );
|
||
|
||
void Cubic_Spline_NormalizeX(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector& output );
|
||
|
||
// See link at Kochanek_Bartels_Spline for info on the basis matrix used
|
||
void BSpline(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector& output );
|
||
|
||
void BSpline_NormalizeX(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector& output );
|
||
|
||
// See link at Kochanek_Bartels_Spline for info on the basis matrix used
|
||
void Parabolic_Spline(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector& output );
|
||
|
||
void Parabolic_Spline_NormalizeX(
|
||
const Vector &p1,
|
||
const Vector &p2,
|
||
const Vector &p3,
|
||
const Vector &p4,
|
||
float t,
|
||
Vector& output );
|
||
|
||
// quintic interpolating polynomial from Perlin.
|
||
// 0->0, 1->1, smooth-in between with smooth tangents
|
||
FORCEINLINE float QuinticInterpolatingPolynomial(float t)
|
||
{
|
||
// 6t^5-15t^4+10t^3
|
||
return t * t * t *( t * ( t* 6.0 - 15.0 ) + 10.0 );
|
||
}
|
||
|
||
// given a table of sorted tabulated positions, return the two indices and blendfactor to linear
|
||
// interpolate. Does a search. Can be used to find the blend value to interpolate between
|
||
// keyframes.
|
||
void GetInterpolationData( float const *pKnotPositions,
|
||
float const *pKnotValues,
|
||
int nNumValuesinList,
|
||
int nInterpolationRange,
|
||
float flPositionToInterpolateAt,
|
||
bool bWrap,
|
||
float *pValueA,
|
||
float *pValueB,
|
||
float *pInterpolationValue);
|
||
|
||
float RangeCompressor( float flValue, float flMin, float flMax, float flBase );
|
||
|
||
// Get the minimum distance from vOrigin to the bounding box defined by [mins,maxs]
|
||
// using voronoi regions.
|
||
// 0 is returned if the origin is inside the box.
|
||
float CalcSqrDistanceToAABB( const Vector &mins, const Vector &maxs, const Vector &point );
|
||
void CalcClosestPointOnAABB( const Vector &mins, const Vector &maxs, const Vector &point, Vector &closestOut );
|
||
void CalcSqrDistAndClosestPointOnAABB( const Vector &mins, const Vector &maxs, const Vector &point, Vector &closestOut, float &distSqrOut );
|
||
|
||
inline float CalcDistanceToAABB( const Vector &mins, const Vector &maxs, const Vector &point )
|
||
{
|
||
float flDistSqr = CalcSqrDistanceToAABB( mins, maxs, point );
|
||
return sqrt(flDistSqr);
|
||
}
|
||
|
||
// Get the closest point from P to the (infinite) line through vLineA and vLineB and
|
||
// calculate the shortest distance from P to the line.
|
||
// If you pass in a value for t, it will tell you the t for (A + (B-A)t) to get the closest point.
|
||
// If the closest point lies on the segment between A and B, then 0 <= t <= 1.
|
||
void CalcClosestPointOnLine( const Vector &P, const Vector &vLineA, const Vector &vLineB, Vector &vClosest, float *t=0 );
|
||
float CalcDistanceToLine( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *t=0 );
|
||
float CalcDistanceSqrToLine( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *t=0 );
|
||
|
||
// The same three functions as above, except now the line is closed between A and B.
|
||
void CalcClosestPointOnLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, Vector &vClosest, float *t=0 );
|
||
float CalcDistanceToLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *t=0 );
|
||
float CalcDistanceSqrToLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *t=0 );
|
||
|
||
// A function to compute the closes line segment connnection two lines (or false if the lines are parallel, etc.)
|
||
bool CalcLineToLineIntersectionSegment(
|
||
const Vector& p1,const Vector& p2,const Vector& p3,const Vector& p4,Vector *s1,Vector *s2,
|
||
float *t1, float *t2 );
|
||
|
||
// The above functions in 2D
|
||
void CalcClosestPointOnLine2D( Vector2D const &P, Vector2D const &vLineA, Vector2D const &vLineB, Vector2D &vClosest, float *t=0 );
|
||
float CalcDistanceToLine2D( Vector2D const &P, Vector2D const &vLineA, Vector2D const &vLineB, float *t=0 );
|
||
float CalcDistanceSqrToLine2D( Vector2D const &P, Vector2D const &vLineA, Vector2D const &vLineB, float *t=0 );
|
||
void CalcClosestPointOnLineSegment2D( Vector2D const &P, Vector2D const &vLineA, Vector2D const &vLineB, Vector2D &vClosest, float *t=0 );
|
||
float CalcDistanceToLineSegment2D( Vector2D const &P, Vector2D const &vLineA, Vector2D const &vLineB, float *t=0 );
|
||
float CalcDistanceSqrToLineSegment2D( Vector2D const &P, Vector2D const &vLineA, Vector2D const &vLineB, float *t=0 );
|
||
|
||
// Init the mathlib
|
||
void MathLib_Init( float gamma = 2.2f, float texGamma = 2.2f, float brightness = 0.0f, int overbright = 2.0f, bool bAllow3DNow = true, bool bAllowSSE = true, bool bAllowSSE2 = true, bool bAllowMMX = true );
|
||
bool MathLib_3DNowEnabled( void );
|
||
bool MathLib_MMXEnabled( void );
|
||
bool MathLib_SSEEnabled( void );
|
||
bool MathLib_SSE2Enabled( void );
|
||
|
||
float Approach( float target, float value, float speed );
|
||
float ApproachAngle( float target, float value, float speed );
|
||
float AngleDiff( float destAngle, float srcAngle );
|
||
float AngleDistance( float next, float cur );
|
||
float AngleNormalize( float angle );
|
||
|
||
// ensure that 0 <= angle <= 360
|
||
float AngleNormalizePositive( float angle );
|
||
|
||
bool AnglesAreEqual( float a, float b, float tolerance = 0.0f );
|
||
|
||
|
||
void RotationDeltaAxisAngle( const QAngle &srcAngles, const QAngle &destAngles, Vector &deltaAxis, float &deltaAngle );
|
||
void RotationDelta( const QAngle &srcAngles, const QAngle &destAngles, QAngle *out );
|
||
|
||
void ComputeTrianglePlane( const Vector& v1, const Vector& v2, const Vector& v3, Vector& normal, float& intercept );
|
||
int PolyFromPlane( Vector *outVerts, const Vector& normal, float dist, float fHalfScale = 9000.0f );
|
||
int ClipPolyToPlane( Vector *inVerts, int vertCount, Vector *outVerts, const Vector& normal, float dist, float fOnPlaneEpsilon = 0.1f );
|
||
int ClipPolyToPlane_Precise( double *inVerts, int vertCount, double *outVerts, const double *normal, double dist, double fOnPlaneEpsilon = 0.1 );
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// Computes a reasonable tangent space for a triangle
|
||
//-----------------------------------------------------------------------------
|
||
void CalcTriangleTangentSpace( const Vector &p0, const Vector &p1, const Vector &p2,
|
||
const Vector2D &t0, const Vector2D &t1, const Vector2D& t2,
|
||
Vector &sVect, Vector &tVect );
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// Transforms a AABB into another space; which will inherently grow the box.
|
||
//-----------------------------------------------------------------------------
|
||
void TransformAABB( const matrix3x4_t &in1, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut );
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// Uses the inverse transform of in1
|
||
//-----------------------------------------------------------------------------
|
||
void ITransformAABB( const matrix3x4_t &in1, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut );
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// Rotates a AABB into another space; which will inherently grow the box.
|
||
// (same as TransformAABB, but doesn't take the translation into account)
|
||
//-----------------------------------------------------------------------------
|
||
void RotateAABB( const matrix3x4_t &in1, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut );
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// Uses the inverse transform of in1
|
||
//-----------------------------------------------------------------------------
|
||
void IRotateAABB( const matrix3x4_t &in1, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut );
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// Transform a plane
|
||
//-----------------------------------------------------------------------------
|
||
inline void MatrixTransformPlane( const matrix3x4_t &src, const cplane_t &inPlane, cplane_t &outPlane )
|
||
{
|
||
// What we want to do is the following:
|
||
// 1) transform the normal into the new space.
|
||
// 2) Determine a point on the old plane given by plane dist * plane normal
|
||
// 3) Transform that point into the new space
|
||
// 4) Plane dist = DotProduct( new normal, new point )
|
||
|
||
// An optimized version, which works if the plane is orthogonal.
|
||
// 1) Transform the normal into the new space
|
||
// 2) Realize that transforming the old plane point into the new space
|
||
// is given by [ d * n'x + Tx, d * n'y + Ty, d * n'z + Tz ]
|
||
// where d = old plane dist, n' = transformed normal, Tn = translational component of transform
|
||
// 3) Compute the new plane dist using the dot product of the normal result of #2
|
||
|
||
// For a correct result, this should be an inverse-transpose matrix
|
||
// but that only matters if there are nonuniform scale or skew factors in this matrix.
|
||
VectorRotate( inPlane.normal, src, outPlane.normal );
|
||
outPlane.dist = inPlane.dist * DotProduct( outPlane.normal, outPlane.normal );
|
||
outPlane.dist += outPlane.normal.x * src[0][3] + outPlane.normal.y * src[1][3] + outPlane.normal.z * src[2][3];
|
||
}
|
||
|
||
inline void MatrixITransformPlane( const matrix3x4_t &src, const cplane_t &inPlane, cplane_t &outPlane )
|
||
{
|
||
// The trick here is that Tn = translational component of transform,
|
||
// but for an inverse transform, Tn = - R^-1 * T
|
||
Vector vecTranslation;
|
||
MatrixGetColumn( src, 3, vecTranslation );
|
||
|
||
Vector vecInvTranslation;
|
||
VectorIRotate( vecTranslation, src, vecInvTranslation );
|
||
|
||
VectorIRotate( inPlane.normal, src, outPlane.normal );
|
||
outPlane.dist = inPlane.dist * DotProduct( outPlane.normal, outPlane.normal );
|
||
outPlane.dist -= outPlane.normal.x * vecInvTranslation[0] + outPlane.normal.y * vecInvTranslation[1] + outPlane.normal.z * vecInvTranslation[2];
|
||
}
|
||
|
||
int CeilPow2( int in );
|
||
int FloorPow2( int in );
|
||
|
||
FORCEINLINE float * UnpackNormal_HEND3N( const unsigned int *pPackedNormal, float *pNormal )
|
||
{
|
||
int temp[3];
|
||
temp[0] = ((*pPackedNormal >> 0L) & 0x7ff);
|
||
if ( temp[0] & 0x400 )
|
||
{
|
||
temp[0] = 2048 - temp[0];
|
||
}
|
||
temp[1] = ((*pPackedNormal >> 11L) & 0x7ff);
|
||
if ( temp[1] & 0x400 )
|
||
{
|
||
temp[1] = 2048 - temp[1];
|
||
}
|
||
temp[2] = ((*pPackedNormal >> 22L) & 0x3ff);
|
||
if ( temp[2] & 0x200 )
|
||
{
|
||
temp[2] = 1024 - temp[2];
|
||
}
|
||
pNormal[0] = (float)temp[0] * 1.0f/1023.0f;
|
||
pNormal[1] = (float)temp[1] * 1.0f/1023.0f;
|
||
pNormal[2] = (float)temp[2] * 1.0f/511.0f;
|
||
return pNormal;
|
||
}
|
||
|
||
FORCEINLINE unsigned int * PackNormal_HEND3N( const float *pNormal, unsigned int *pPackedNormal )
|
||
{
|
||
int temp[3];
|
||
|
||
temp[0] = Float2Int( pNormal[0] * 1023.0f );
|
||
temp[1] = Float2Int( pNormal[1] * 1023.0f );
|
||
temp[2] = Float2Int( pNormal[2] * 511.0f );
|
||
|
||
// the normal is out of bounds, determine the source and fix
|
||
// clamping would be even more of a slowdown here
|
||
Assert( temp[0] >= -1023 && temp[0] <= 1023 );
|
||
Assert( temp[1] >= -1023 && temp[1] <= 1023 );
|
||
Assert( temp[2] >= -511 && temp[2] <= 511 );
|
||
|
||
*pPackedNormal = ( ( temp[2] & 0x3ff ) << 22L ) |
|
||
( ( temp[1] & 0x7ff ) << 11L ) |
|
||
( ( temp[0] & 0x7ff ) << 0L );
|
||
return pPackedNormal;
|
||
}
|
||
|
||
FORCEINLINE unsigned int * PackNormal_HEND3N( float nx, float ny, float nz, unsigned int *pPackedNormal )
|
||
{
|
||
int temp[3];
|
||
|
||
temp[0] = Float2Int( nx * 1023.0f );
|
||
temp[1] = Float2Int( ny * 1023.0f );
|
||
temp[2] = Float2Int( nz * 511.0f );
|
||
|
||
// the normal is out of bounds, determine the source and fix
|
||
// clamping would be even more of a slowdown here
|
||
Assert( temp[0] >= -1023 && temp[0] <= 1023 );
|
||
Assert( temp[1] >= -1023 && temp[1] <= 1023 );
|
||
Assert( temp[2] >= -511 && temp[2] <= 511 );
|
||
|
||
*pPackedNormal = ( ( temp[2] & 0x3ff ) << 22L ) |
|
||
( ( temp[1] & 0x7ff ) << 11L ) |
|
||
( ( temp[0] & 0x7ff ) << 0L );
|
||
return pPackedNormal;
|
||
}
|
||
|
||
FORCEINLINE float * UnpackNormal_SHORT2( const unsigned int *pPackedNormal, float *pNormal, bool bIsTangent = FALSE )
|
||
{
|
||
// Unpacks from Jason's 2-short format (fills in a 4th binormal-sign (+1/-1) value, if this is a tangent vector)
|
||
|
||
// FIXME: short math is slow on 360 - use ints here instead (bit-twiddle to deal w/ the sign bits)
|
||
short iX = (*pPackedNormal & 0x0000FFFF);
|
||
short iY = (*pPackedNormal & 0xFFFF0000) >> 16;
|
||
|
||
float zSign = +1;
|
||
if ( iX < 0 )
|
||
{
|
||
zSign = -1;
|
||
iX = -iX;
|
||
}
|
||
float tSign = +1;
|
||
if ( iY < 0 )
|
||
{
|
||
tSign = -1;
|
||
iY = -iY;
|
||
}
|
||
|
||
pNormal[0] = ( iX - 16384.0f ) / 16384.0f;
|
||
pNormal[1] = ( iY - 16384.0f ) / 16384.0f;
|
||
pNormal[2] = zSign*sqrtf( 1.0f - ( pNormal[0]*pNormal[0] + pNormal[1]*pNormal[1] ) );
|
||
if ( bIsTangent )
|
||
{
|
||
pNormal[3] = tSign;
|
||
}
|
||
|
||
return pNormal;
|
||
}
|
||
|
||
FORCEINLINE unsigned int * PackNormal_SHORT2( float nx, float ny, float nz, unsigned int *pPackedNormal, float binormalSign = +1.0f )
|
||
{
|
||
// Pack a vector (ASSUMED TO BE NORMALIZED) into Jason's 4-byte (SHORT2) format.
|
||
// This simply reconstructs Z from X & Y. It uses the sign bits of the X & Y coords
|
||
// to reconstruct the sign of Z and, if this is a tangent vector, the sign of the
|
||
// binormal (this is needed because tangent/binormal vectors are supposed to follow
|
||
// UV gradients, but shaders reconstruct the binormal from the tangent and normal
|
||
// assuming that they form a right-handed basis).
|
||
|
||
nx += 1; // [-1,+1] -> [0,2]
|
||
ny += 1;
|
||
nx *= 16384.0f; // [ 0, 2] -> [0,32768]
|
||
ny *= 16384.0f;
|
||
|
||
// '0' and '32768' values are invalid encodings
|
||
nx = max( nx, 1.0f ); // Make sure there are no zero values
|
||
ny = max( ny, 1.0f );
|
||
nx = min( nx, 32767.0f ); // Make sure there are no 32768 values
|
||
ny = min( ny, 32767.0f );
|
||
|
||
if ( nz < 0.0f )
|
||
nx = -nx; // Set the sign bit for z
|
||
|
||
ny *= binormalSign; // Set the sign bit for the binormal (use when encoding a tangent vector)
|
||
|
||
// FIXME: short math is slow on 360 - use ints here instead (bit-twiddle to deal w/ the sign bits), also use Float2Int()
|
||
short sX = (short)nx; // signed short [1,32767]
|
||
short sY = (short)ny;
|
||
|
||
*pPackedNormal = ( sX & 0x0000FFFF ) | ( sY << 16 ); // NOTE: The mask is necessary (if sX is negative and cast to an int...)
|
||
|
||
return pPackedNormal;
|
||
}
|
||
|
||
FORCEINLINE unsigned int * PackNormal_SHORT2( const float *pNormal, unsigned int *pPackedNormal, float binormalSign = +1.0f )
|
||
{
|
||
return PackNormal_SHORT2( pNormal[0], pNormal[1], pNormal[2], pPackedNormal, binormalSign );
|
||
}
|
||
|
||
// Unpacks a UBYTE4 normal (for a tangent, the result's fourth component receives the binormal 'sign')
|
||
FORCEINLINE float * UnpackNormal_UBYTE4( const unsigned int *pPackedNormal, float *pNormal, bool bIsTangent = FALSE )
|
||
{
|
||
unsigned char cX, cY;
|
||
if ( bIsTangent )
|
||
{
|
||
cX = *pPackedNormal >> 16; // Unpack Z
|
||
cY = *pPackedNormal >> 24; // Unpack W
|
||
}
|
||
else
|
||
{
|
||
cX = *pPackedNormal >> 0; // Unpack X
|
||
cY = *pPackedNormal >> 8; // Unpack Y
|
||
}
|
||
|
||
float x = cX - 128.0f;
|
||
float y = cY - 128.0f;
|
||
float z;
|
||
|
||
float zSignBit = x < 0 ? 1.0f : 0.0f; // z and t negative bits (like slt asm instruction)
|
||
float tSignBit = y < 0 ? 1.0f : 0.0f;
|
||
float zSign = -( 2*zSignBit - 1 ); // z and t signs
|
||
float tSign = -( 2*tSignBit - 1 );
|
||
|
||
x = x*zSign - zSignBit; // 0..127
|
||
y = y*tSign - tSignBit;
|
||
x = x - 64; // -64..63
|
||
y = y - 64;
|
||
|
||
float xSignBit = x < 0 ? 1.0f : 0.0f; // x and y negative bits (like slt asm instruction)
|
||
float ySignBit = y < 0 ? 1.0f : 0.0f;
|
||
float xSign = -( 2*xSignBit - 1 ); // x and y signs
|
||
float ySign = -( 2*ySignBit - 1 );
|
||
|
||
x = ( x*xSign - xSignBit ) / 63.0f; // 0..1 range
|
||
y = ( y*ySign - ySignBit ) / 63.0f;
|
||
z = 1.0f - x - y;
|
||
|
||
float oolen = 1.0f / sqrt( x*x + y*y + z*z ); // Normalize and
|
||
x *= oolen * xSign; // Recover signs
|
||
y *= oolen * ySign;
|
||
z *= oolen * zSign;
|
||
|
||
pNormal[0] = x;
|
||
pNormal[1] = y;
|
||
pNormal[2] = z;
|
||
if ( bIsTangent )
|
||
{
|
||
pNormal[3] = tSign;
|
||
}
|
||
|
||
return pNormal;
|
||
}
|
||
|
||
//////////////////////////////////////////////////////////////////////////////
|
||
// See: http://www.oroboro.com/rafael/docserv.php/index/programming/article/unitv2
|
||
//
|
||
// UBYTE4 encoding, using per-octant projection onto x+y+z=1
|
||
// Assume input vector is already unit length
|
||
//
|
||
// binormalSign specifies 'sign' of binormal, stored in t sign bit of tangent
|
||
// (lets the shader know whether norm/tan/bin form a right-handed basis)
|
||
//
|
||
// bIsTangent is used to specify which WORD of the output to store the data
|
||
// The expected usage is to call once with the normal and once with
|
||
// the tangent and binormal sign flag, bitwise OR'ing the returned DWORDs
|
||
FORCEINLINE unsigned int * PackNormal_UBYTE4( float nx, float ny, float nz, unsigned int *pPackedNormal, bool bIsTangent = false, float binormalSign = +1.0f )
|
||
{
|
||
float xSign = nx < 0.0f ? -1.0f : 1.0f; // -1 or 1 sign
|
||
float ySign = ny < 0.0f ? -1.0f : 1.0f;
|
||
float zSign = nz < 0.0f ? -1.0f : 1.0f;
|
||
float tSign = binormalSign;
|
||
Assert( ( binormalSign == +1.0f ) || ( binormalSign == -1.0f ) );
|
||
|
||
float xSignBit = 0.5f*( 1 - xSign ); // [-1,+1] -> [1,0]
|
||
float ySignBit = 0.5f*( 1 - ySign ); // 1 is negative bit (like slt instruction)
|
||
float zSignBit = 0.5f*( 1 - zSign );
|
||
float tSignBit = 0.5f*( 1 - binormalSign );
|
||
|
||
float absX = xSign*nx; // 0..1 range (abs)
|
||
float absY = ySign*ny;
|
||
float absZ = zSign*nz;
|
||
|
||
float xbits = absX / ( absX + absY + absZ ); // Project onto x+y+z=1 plane
|
||
float ybits = absY / ( absX + absY + absZ );
|
||
|
||
xbits *= 63; // 0..63
|
||
ybits *= 63;
|
||
|
||
xbits = xbits * xSign - xSignBit; // -64..63 range
|
||
ybits = ybits * ySign - ySignBit;
|
||
xbits += 64.0f; // 0..127 range
|
||
ybits += 64.0f;
|
||
|
||
xbits = xbits * zSign - zSignBit; // Negate based on z and t
|
||
ybits = ybits * tSign - tSignBit; // -128..127 range
|
||
|
||
xbits += 128.0f; // 0..255 range
|
||
ybits += 128.0f;
|
||
|
||
unsigned char cX = (unsigned char) xbits;
|
||
unsigned char cY = (unsigned char) ybits;
|
||
|
||
if ( !bIsTangent )
|
||
*pPackedNormal = (cX << 0) | (cY << 8); // xy for normal
|
||
else
|
||
*pPackedNormal = (cX << 16) | (cY << 24); // zw for tangent
|
||
|
||
return pPackedNormal;
|
||
}
|
||
|
||
FORCEINLINE unsigned int * PackNormal_UBYTE4( const float *pNormal, unsigned int *pPackedNormal, bool bIsTangent = false, float binormalSign = +1.0f )
|
||
{
|
||
return PackNormal_UBYTE4( pNormal[0], pNormal[1], pNormal[2], pPackedNormal, bIsTangent, binormalSign );
|
||
}
|
||
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// Convert RGB to HSV
|
||
//-----------------------------------------------------------------------------
|
||
void RGBtoHSV( const Vector &rgb, Vector &hsv );
|
||
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// Convert HSV to RGB
|
||
//-----------------------------------------------------------------------------
|
||
void HSVtoRGB( const Vector &hsv, Vector &rgb );
|
||
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// Fast version of pow and log
|
||
//-----------------------------------------------------------------------------
|
||
|
||
float FastLog2(float i); // log2( i )
|
||
float FastPow2(float i); // 2^i
|
||
float FastPow(float a, float b); // a^b
|
||
float FastPow10( float i ); // 10^i
|
||
|
||
//-----------------------------------------------------------------------------
|
||
// For testing float equality
|
||
//-----------------------------------------------------------------------------
|
||
|
||
inline bool CloseEnough( float a, float b, float epsilon = EQUAL_EPSILON )
|
||
{
|
||
return fabs( a - b ) <= epsilon;
|
||
}
|
||
|
||
inline bool CloseEnough( const Vector &a, const Vector &b, float epsilon = EQUAL_EPSILON )
|
||
{
|
||
return fabs( a.x - b.x ) <= epsilon &&
|
||
fabs( a.y - b.y ) <= epsilon &&
|
||
fabs( a.z - b.z ) <= epsilon;
|
||
}
|
||
|
||
// Fast compare
|
||
// maxUlps is the maximum error in terms of Units in the Last Place. This
|
||
// specifies how big an error we are willing to accept in terms of the value
|
||
// of the least significant digit of the floating point number<65>s
|
||
// representation. maxUlps can also be interpreted in terms of how many
|
||
// representable floats we are willing to accept between A and B.
|
||
// This function will allow maxUlps-1 floats between A and B.
|
||
bool AlmostEqual(float a, float b, int maxUlps = 10);
|
||
|
||
inline bool AlmostEqual( const Vector &a, const Vector &b, int maxUlps = 10)
|
||
{
|
||
return AlmostEqual( a.x, b.x, maxUlps ) &&
|
||
AlmostEqual( a.y, b.y, maxUlps ) &&
|
||
AlmostEqual( a.z, b.z, maxUlps );
|
||
}
|
||
|
||
|
||
#endif // MATH_BASE_H
|
||
|