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+// Math3d.h
+// Header file for the Math3d library. The C-Runtime has math.h, this file and the
+// accompanying math.c are meant to suppliment math.h by adding geometry/math routines
+// useful for graphics, simulation, and physics applications (3D stuff).
+// Richard S. Wright Jr.
+#ifndef _MATH3D_LIBRARY__
+#define _MATH3D_LIBRARY__
+
+#include <math.h>
+#include <memory.h>
+
+///////////////////////////////////////////////////////////////////////////////
+// Data structures and containers
+// Much thought went into how these are declared. Many libraries declare these
+// as structures with x, y, z data members. However structure alignment issues
+// could limit the portability of code based on such structures, or the binary
+// compatibility of data files (more likely) that contain such structures across
+// compilers/platforms. Arrays are always tightly packed, and are more efficient
+// for moving blocks of data around (usually).
+typedef float M3DVector3f[3]; // Vector of three floats (x, y, z)
+typedef double M3DVector3d[3]; // Vector of three doubles (x, y, z)
+
+typedef float M3DVector4f[4]; // Lesser used... Do we really need these?
+typedef double M3DVector4d[4]; // Yes, occasionaly
+
+typedef float M3DVector2f[2]; // 3D points = 3D Vectors, but we need a
+typedef double M3DVector2d[2]; // 2D representations sometimes... (x,y) order
+
+
+
+// 3x3 matrix - column major. X vector is 0, 1, 2, etc.
+// 0 3 6
+// 1 4 7
+// 2 5 8
+typedef float M3DMatrix33f[9]; // A 3 x 3 matrix, column major (floats) - OpenGL Style
+typedef double M3DMatrix33d[9]; // A 3 x 3 matrix, column major (doubles) - OpenGL Style
+
+
+// 4x4 matrix - column major. X vector is 0, 1, 2, etc.
+// 0 4 8 12
+// 1 5 9 13
+// 2 6 10 14
+// 3 7 11 15
+typedef float M3DMatrix44f[16]; // A 4 X 4 matrix, column major (floats) - OpenGL style
+typedef double M3DMatrix44d[16]; // A 4 x 4 matrix, column major (doubles) - OpenGL style
+
+
+///////////////////////////////////////////////////////////////////////////////
+// Useful constants
+#define M3D_PI (3.14159265358979323846)
+#define M3D_2PI (2.0 * M3D_PI)
+#define M3D_PI_DIV_180 (0.017453292519943296)
+#define M3D_INV_PI_DIV_180 (57.2957795130823229)
+
+
+///////////////////////////////////////////////////////////////////////////////
+// Useful shortcuts and macros
+// Radians are king... but we need a way to swap back and forth
+#define m3dDegToRad(x) ((x)*M3D_PI_DIV_180)
+#define m3dRadToDeg(x) ((x)*M3D_INV_PI_DIV_180)
+
+// Hour angles
+#define m3dHrToDeg(x) ((x) * (1.0 / 15.0))
+#define m3dHrToRad(x) m3dDegToRad(m3dHrToDeg(x))
+
+#define m3dDegToHr(x) ((x) * 15.0))
+#define m3dRadToHr(x) m3dDegToHr(m3dRadToDeg(x))
+
+
+// Returns the same number if it is a power of
+// two. Returns a larger integer if it is not a
+// power of two. The larger integer is the next
+// highest power of two.
+inline unsigned int m3dIsPOW2(unsigned int iValue)
+ {
+ unsigned int nPow2 = 1;
+
+ while(iValue > nPow2)
+ nPow2 = (nPow2 << 1);
+
+ return nPow2;
+ }
+
+
+///////////////////////////////////////////////////////////////////////////////
+// Inline accessor functions for people who just can't count to 3 - Vectors
+#define m3dGetVectorX(v) (v[0])
+#define m3dGetVectorY(v) (v[1])
+#define m3dGetVectorZ(v) (v[2])
+#define m3dGetVectorW(v) (v[3])
+
+#define m3dSetVectorX(v, x) ((v)[0] = (x))
+#define m3dSetVectorY(v, y) ((v)[1] = (y))
+#define m3dSetVectorZ(v, z) ((v)[2] = (z))
+#define m3dSetVectorW(v, w) ((v)[3] = (w))
+
+///////////////////////////////////////////////////////////////////////////////
+// Inline vector functions
+// Load Vector with (x, y, z, w).
+inline void m3dLoadVector2(M3DVector2f v, float x, float y)
+ { v[0] = x; v[1] = y; }
+inline void m3dLoadVector2(M3DVector2d v, float x, float y)
+ { v[0] = x; v[1] = y; }
+inline void m3dLoadVector3(M3DVector3f v, float x, float y, float z)
+ { v[0] = x; v[1] = y; v[2] = z; }
+inline void m3dLoadVector3(M3DVector3d v, double x, double y, double z)
+ { v[0] = x; v[1] = y; v[2] = z; }
+inline void m3dLoadVector4(M3DVector4f v, float x, float y, float z, float w)
+ { v[0] = x; v[1] = y; v[2] = z; v[3] = w;}
+inline void m3dLoadVector4(M3DVector4d v, double x, double y, double z, double w)
+ { v[0] = x; v[1] = y; v[2] = z; v[3] = w;}
+
+
+////////////////////////////////////////////////////////////////////////////////
+// Copy vector src into vector dst
+inline void m3dCopyVector2(M3DVector2f dst, const M3DVector2f src) { memcpy(dst, src, sizeof(M3DVector2f)); }
+inline void m3dCopyVector2(M3DVector2d dst, const M3DVector2d src) { memcpy(dst, src, sizeof(M3DVector2d)); }
+
+inline void m3dCopyVector3(M3DVector3f dst, const M3DVector3f src) { memcpy(dst, src, sizeof(M3DVector3f)); }
+inline void m3dCopyVector3(M3DVector3d dst, const M3DVector3d src) { memcpy(dst, src, sizeof(M3DVector3d)); }
+
+inline void m3dCopyVector4(M3DVector4f dst, const M3DVector4f src) { memcpy(dst, src, sizeof(M3DVector4f)); }
+inline void m3dCopyVector4(M3DVector4d dst, const M3DVector4d src) { memcpy(dst, src, sizeof(M3DVector4d)); }
+
+
+////////////////////////////////////////////////////////////////////////////////
+// Add Vectors (r, a, b) r = a + b
+inline void m3dAddVectors2(M3DVector2f r, const M3DVector2f a, const M3DVector2f b)
+ { r[0] = a[0] + b[0]; r[1] = a[1] + b[1]; }
+inline void m3dAddVectors2(M3DVector2d r, const M3DVector2d a, const M3DVector2d b)
+ { r[0] = a[0] + b[0]; r[1] = a[1] + b[1]; }
+
+inline void m3dAddVectors3(M3DVector3f r, const M3DVector3f a, const M3DVector3f b)
+ { r[0] = a[0] + b[0]; r[1] = a[1] + b[1]; r[2] = a[2] + b[2]; }
+inline void m3dAddVectors3(M3DVector3d r, const M3DVector3d a, const M3DVector3d b)
+ { r[0] = a[0] + b[0]; r[1] = a[1] + b[1]; r[2] = a[2] + b[2]; }
+
+inline void m3dAddVectors4(M3DVector4f r, const M3DVector4f a, const M3DVector4f b)
+ { r[0] = a[0] + b[0]; r[1] = a[1] + b[1]; r[2] = a[2] + b[2]; r[3] = a[3] + b[3]; }
+inline void m3dAddVectors4(M3DVector4d r, const M3DVector4d a, const M3DVector4d b)
+ { r[0] = a[0] + b[0]; r[1] = a[1] + b[1]; r[2] = a[2] + b[2]; r[3] = a[3] + b[3]; }
+
+////////////////////////////////////////////////////////////////////////////////
+// Subtract Vectors (r, a, b) r = a - b
+inline void m3dSubtractVectors2(M3DVector2f r, const M3DVector2f a, const M3DVector2f b)
+ { r[0] = a[0] - b[0]; r[1] = a[1] - b[1]; }
+inline void m3dSubtractVectors2(M3DVector2d r, const M3DVector2d a, const M3DVector2d b)
+ { r[0] = a[0] - b[0]; r[1] = a[1] - b[1]; }
+
+inline void m3dSubtractVectors3(M3DVector3f r, const M3DVector3f a, const M3DVector3f b)
+ { r[0] = a[0] - b[0]; r[1] = a[1] - b[1]; r[2] = a[2] - b[2]; }
+inline void m3dSubtractVectors3(M3DVector3d r, const M3DVector3d a, const M3DVector3d b)
+ { r[0] = a[0] - b[0]; r[1] = a[1] - b[1]; r[2] = a[2] - b[2]; }
+
+inline void m3dSubtractVectors4(M3DVector4f r, const M3DVector4f a, const M3DVector4f b)
+ { r[0] = a[0] - b[0]; r[1] = a[1] - b[1]; r[2] = a[2] - b[2]; r[3] = a[3] - b[3]; }
+inline void m3dSubtractVectors4(M3DVector4d r, const M3DVector4d a, const M3DVector4d b)
+ { r[0] = a[0] - b[0]; r[1] = a[1] - b[1]; r[2] = a[2] - b[2]; r[3] = a[3] - b[3]; }
+
+
+
+///////////////////////////////////////////////////////////////////////////////////////
+// Scale Vectors (in place)
+inline void m3dScaleVector2(M3DVector2f v, float scale)
+ { v[0] *= scale; v[1] *= scale; }
+inline void m3dScaleVector2(M3DVector2d v, double scale)
+ { v[0] *= scale; v[1] *= scale; }
+
+inline void m3dScaleVector3(M3DVector3f v, float scale)
+ { v[0] *= scale; v[1] *= scale; v[2] *= scale; }
+inline void m3dScaleVector3(M3DVector3d v, double scale)
+ { v[0] *= scale; v[1] *= scale; v[2] *= scale; }
+
+inline void m3dScaleVector4(M3DVector4f v, float scale)
+ { v[0] *= scale; v[1] *= scale; v[2] *= scale; v[3] *= scale; }
+inline void m3dScaleVector4(M3DVector4d v, double scale)
+ { v[0] *= scale; v[1] *= scale; v[2] *= scale; v[3] *= scale; }
+
+
+//////////////////////////////////////////////////////////////////////////////////////
+// Cross Product
+// u x v = result
+// We only need one version for floats, and one version for doubles. A 3 component
+// vector fits in a 4 component vector. If M3DVector4d or M3DVector4f are passed
+// we will be OK because 4th component is not used.
+inline void m3dCrossProduct(M3DVector3f result, const M3DVector3f u, const M3DVector3f v)
+ {
+ result[0] = u[1]*v[2] - v[1]*u[2];
+ result[1] = -u[0]*v[2] + v[0]*u[2];
+ result[2] = u[0]*v[1] - v[0]*u[1];
+ }
+
+inline void m3dCrossProduct(M3DVector3d result, const M3DVector3d u, const M3DVector3d v)
+ {
+ result[0] = u[1]*v[2] - v[1]*u[2];
+ result[1] = -u[0]*v[2] + v[0]*u[2];
+ result[2] = u[0]*v[1] - v[0]*u[1];
+ }
+
+//////////////////////////////////////////////////////////////////////////////////////
+// Dot Product, only for three component vectors
+// return u dot v
+inline float m3dDotProduct(const M3DVector3f u, const M3DVector3f v)
+ { return u[0]*v[0] + u[1]*v[1] + u[2]*v[2]; }
+
+inline double m3dDotProduct(const M3DVector3d u, const M3DVector3d v)
+ { return u[0]*v[0] + u[1]*v[1] + u[2]*v[2]; }
+
+//////////////////////////////////////////////////////////////////////////////////////
+// Angle between vectors, only for three component vectors. Angle is in radians...
+inline float m3dGetAngleBetweenVectors(const M3DVector3f u, const M3DVector3f v)
+ {
+ float dTemp = m3dDotProduct(u, v);
+ return float(acos(double(dTemp)));
+ }
+
+inline double m3dGetAngleBetweenVectors(const M3DVector3d u, const M3DVector3d v)
+ {
+ double dTemp = m3dDotProduct(u, v);
+ return acos(dTemp);
+ }
+
+//////////////////////////////////////////////////////////////////////////////////////
+// Get Square of a vectors length
+// Only for three component vectors
+inline float m3dGetVectorLengthSquared(const M3DVector3f u)
+ { return (u[0] * u[0]) + (u[1] * u[1]) + (u[2] * u[2]); }
+
+inline double m3dGetVectorLengthSquared(const M3DVector3d u)
+ { return (u[0] * u[0]) + (u[1] * u[1]) + (u[2] * u[2]); }
+
+//////////////////////////////////////////////////////////////////////////////////////
+// Get lenght of vector
+// Only for three component vectors.
+inline float m3dGetVectorLength(const M3DVector3f u)
+ { return float(sqrt(double(m3dGetVectorLengthSquared(u)))); }
+
+inline double m3dGetVectorLength(const M3DVector3d u)
+ { return sqrt(m3dGetVectorLengthSquared(u)); }
+
+//////////////////////////////////////////////////////////////////////////////////////
+// Normalize a vector
+// Scale a vector to unit length. Easy, just scale the vector by it's length
+inline void m3dNormalizeVector(M3DVector3f u)
+ { m3dScaleVector3(u, 1.0f / m3dGetVectorLength(u)); }
+
+inline void m3dNormalizeVector(M3DVector3d u)
+ { m3dScaleVector3(u, 1.0 / m3dGetVectorLength(u)); }
+
+
+//////////////////////////////////////////////////////////////////////////////////////
+// Get the distance between two points. The distance between two points is just
+// the magnitude of the difference between two vectors
+// Located in math.cpp
+float m3dGetDistanceSquared(const M3DVector3f u, const M3DVector3f v);
+double m3dGetDistanceSquared(const M3DVector3d u, const M3DVector3d v);
+
+inline double m3dGetDistance(const M3DVector3d u, const M3DVector3d v)
+{ return sqrt(m3dGetDistanceSquared(u, v)); }
+
+inline float m3dGetDistance(const M3DVector3f u, const M3DVector3f v)
+{ return float(sqrt(m3dGetDistanceSquared(u, v))); }
+
+inline float m3dGetMagnitudeSquared(const M3DVector3f u) { return u[0]*u[0] + u[1]*u[1] + u[2]*u[2]; }
+inline double m3dGetMagnitudeSquared(const M3DVector3d u) { return u[0]*u[0] + u[1]*u[1] + u[2]*u[2]; }
+
+inline float m3dGetMagnitude(const M3DVector3f u) { return float(sqrt(m3dGetMagnitudeSquared(u))); }
+inline double m3dGetMagnitude(const M3DVector3d u) { return sqrt(m3dGetMagnitudeSquared(u)); }
+
+
+
+//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Matrix functions
+// Both floating point and double precision 3x3 and 4x4 matricies are supported.
+// No support is included for arbitrarily dimensioned matricies on purpose, since
+// the 3x3 and 4x4 matrix routines are the most common for the purposes of this
+// library. Matrices are column major, like OpenGL matrices.
+// Unlike the vector functions, some of these are going to have to not be inlined,
+// although many will be.
+
+
+// Copy Matrix
+// Brain-dead memcpy
+inline void m3dCopyMatrix33(M3DMatrix33f dst, const M3DMatrix33f src)
+ { memcpy(dst, src, sizeof(M3DMatrix33f)); }
+
+inline void m3dCopyMatrix33(M3DMatrix33d dst, const M3DMatrix33d src)
+ { memcpy(dst, src, sizeof(M3DMatrix33d)); }
+
+inline void m3dCopyMatrix44(M3DMatrix44f dst, const M3DMatrix44f src)
+ { memcpy(dst, src, sizeof(M3DMatrix44f)); }
+
+inline void m3dCopyMatrix44(M3DMatrix44d dst, const M3DMatrix44d src)
+ { memcpy(dst, src, sizeof(M3DMatrix44d)); }
+
+// LoadIdentity
+// Implemented in Math3d.cpp
+void m3dLoadIdentity33(M3DMatrix33f m);
+void m3dLoadIdentity33(M3DMatrix33d m);
+void m3dLoadIdentity44(M3DMatrix44f m);
+void m3dLoadIdentity44(M3DMatrix44d m);
+
+/////////////////////////////////////////////////////////////////////////////
+// Get/Set Column.
+inline void m3dGetMatrixColumn33(M3DVector3f dst, const M3DMatrix33f src, int column)
+ { memcpy(dst, src + (3 * column), sizeof(float) * 3); }
+
+inline void m3dGetMatrixColumn33(M3DVector3d dst, const M3DMatrix33d src, int column)
+ { memcpy(dst, src + (3 * column), sizeof(double) * 3); }
+
+inline void m3dSetMatrixColumn33(M3DMatrix33f dst, const M3DVector3f src, int column)
+ { memcpy(dst + (3 * column), src, sizeof(float) * 3); }
+
+inline void m3dSetMatrixColumn33(M3DMatrix33d dst, const M3DVector3d src, int column)
+ { memcpy(dst + (3 * column), src, sizeof(double) * 3); }
+
+inline void m3dGetMatrixColumn44(M3DVector4f dst, const M3DMatrix44f src, int column)
+ { memcpy(dst, src + (4 * column), sizeof(float) * 4); }
+
+inline void m3dGetMatrixColumn44(M3DVector4d dst, const M3DMatrix44d src, int column)
+ { memcpy(dst, src + (4 * column), sizeof(double) * 4); }
+
+inline void m3dSetMatrixColumn44(M3DMatrix44f dst, const M3DVector4f src, int column)
+ { memcpy(dst + (4 * column), src, sizeof(float) * 4); }
+
+inline void m3dSetMatrixColumn44(M3DMatrix44d dst, const M3DVector4d src, int column)
+ { memcpy(dst + (4 * column), src, sizeof(double) * 4); }
+
+
+// Get/Set row purposely omitted... use the functions below.
+// I don't think row vectors are useful for column major ordering...
+// If I'm wrong, add them later.
+
+
+//////////////////////////////////////////////////////////////////////////////
+// Get/Set RowCol - Remember column major ordering...
+// Provides for element addressing
+inline void m3dSetMatrixRowCol33(M3DMatrix33f m, int row, int col, float value)
+ { m[(col * 3) + row] = value; }
+
+inline float m3dGetMatrixRowCol33(const M3DMatrix33f m, int row, int col)
+ { return m[(col * 3) + row]; }
+
+inline void m3dSetMatrixRowCol33(M3DMatrix33d m, int row, int col, double value)
+ { m[(col * 3) + row] = value; }
+
+inline double m3dGetMatrixRowCol33(const M3DMatrix33d m, int row, int col)
+ { return m[(col * 3) + row]; }
+
+inline void m3dSetMatrixRowCol44(M3DMatrix44f m, int row, int col, float value)
+ { m[(col * 4) + row] = value; }
+
+inline float m3dGetMatrixRowCol44(const M3DMatrix44f m, int row, int col)
+ { return m[(col * 4) + row]; }
+
+inline void m3dSetMatrixRowCol44(M3DMatrix44d m, int row, int col, double value)
+ { m[(col * 4) + row] = value; }
+
+inline double m3dGetMatrixRowCol44(const M3DMatrix44d m, int row, int col)
+ { return m[(col * 4) + row]; }
+
+
+///////////////////////////////////////////////////////////////////////////////
+// Extract a rotation matrix from a 4x4 matrix
+// Extracts the rotation matrix (3x3) from a 4x4 matrix
+inline void m3dExtractRotation(M3DMatrix33f dst, const M3DMatrix44f src)
+ {
+ memcpy(dst, src, sizeof(float) * 3); // X column
+ memcpy(dst + 3, src + 4, sizeof(float) * 3); // Y column
+ memcpy(dst + 6, src + 8, sizeof(float) * 3); // Z column
+ }
+
+// Ditto above, but for doubles
+inline void m3dExtractRotation(M3DMatrix33d dst, const M3DMatrix44d src)
+ {
+ memcpy(dst, src, sizeof(double) * 3); // X column
+ memcpy(dst + 3, src + 4, sizeof(double) * 3); // Y column
+ memcpy(dst + 6, src + 8, sizeof(double) * 3); // Z column
+ }
+
+// Inject Rotation (3x3) into a full 4x4 matrix...
+inline void m3dInjectRotation(M3DMatrix44f dst, const M3DMatrix33f src)
+ {
+ memcpy(dst, src, sizeof(float) * 4);
+ memcpy(dst + 4, src + 4, sizeof(float) * 4);
+ memcpy(dst + 8, src + 8, sizeof(float) * 4);
+ }
+
+// Ditto above for doubles
+inline void m3dInjectRotation(M3DMatrix44d dst, const M3DMatrix33d src)
+ {
+ memcpy(dst, src, sizeof(double) * 4);
+ memcpy(dst + 4, src + 4, sizeof(double) * 4);
+ memcpy(dst + 8, src + 8, sizeof(double) * 4);
+ }
+
+
+////////////////////////////////////////////////////////////////////////////////
+// MultMatrix
+// Implemented in Math.cpp
+void m3dMatrixMultiply44(M3DMatrix44f product, const M3DMatrix44f a, const M3DMatrix44f b);
+void m3dMatrixMultiply44(M3DMatrix44d product, const M3DMatrix44d a, const M3DMatrix44d b);
+void m3dMatrixMultiply33(M3DMatrix33f product, const M3DMatrix33f a, const M3DMatrix33f b);
+void m3dMatrixMultiply33(M3DMatrix33d product, const M3DMatrix33d a, const M3DMatrix33d b);
+
+
+// Transform - Does rotation and translation via a 4x4 matrix. Transforms
+// a point or vector.
+// By-the-way __inline means I'm asking the compiler to do a cost/benefit analysis. If
+// these are used frequently, they may not be inlined to save memory. I'm experimenting
+// with this....
+__inline void m3dTransformVector3(M3DVector3f vOut, const M3DVector3f v, const M3DMatrix44f m)
+ {
+ vOut[0] = m[0] * v[0] + m[4] * v[1] + m[8] * v[2] + m[12];// * v[3];
+ vOut[1] = m[1] * v[0] + m[5] * v[1] + m[9] * v[2] + m[13];// * v[3];
+ vOut[2] = m[2] * v[0] + m[6] * v[1] + m[10] * v[2] + m[14];// * v[3];
+ //vOut[3] = m[3] * v[0] + m[7] * v[1] + m[11] * v[2] + m[15] * v[3];
+ }
+
+// Ditto above, but for doubles
+__inline void m3dTransformVector3(M3DVector3d vOut, const M3DVector3d v, const M3DMatrix44d m)
+ {
+ vOut[0] = m[0] * v[0] + m[4] * v[1] + m[8] * v[2] + m[12];// * v[3];
+ vOut[1] = m[1] * v[0] + m[5] * v[1] + m[9] * v[2] + m[13];// * v[3];
+ vOut[2] = m[2] * v[0] + m[6] * v[1] + m[10] * v[2] + m[14];// * v[3];
+ //vOut[3] = m[3] * v[0] + m[7] * v[1] + m[11] * v[2] + m[15] * v[3];
+ }
+
+__inline void m3dTransformVector4(M3DVector4f vOut, const M3DVector4f v, const M3DMatrix44f m)
+ {
+ vOut[0] = m[0] * v[0] + m[4] * v[1] + m[8] * v[2] + m[12] * v[3];
+ vOut[1] = m[1] * v[0] + m[5] * v[1] + m[9] * v[2] + m[13] * v[3];
+ vOut[2] = m[2] * v[0] + m[6] * v[1] + m[10] * v[2] + m[14] * v[3];
+ vOut[3] = m[3] * v[0] + m[7] * v[1] + m[11] * v[2] + m[15] * v[3];
+ }
+
+// Ditto above, but for doubles
+__inline void m3dTransformVector4(M3DVector4d vOut, const M3DVector4d v, const M3DMatrix44d m)
+ {
+ vOut[0] = m[0] * v[0] + m[4] * v[1] + m[8] * v[2] + m[12] * v[3];
+ vOut[1] = m[1] * v[0] + m[5] * v[1] + m[9] * v[2] + m[13] * v[3];
+ vOut[2] = m[2] * v[0] + m[6] * v[1] + m[10] * v[2] + m[14] * v[3];
+ vOut[3] = m[3] * v[0] + m[7] * v[1] + m[11] * v[2] + m[15] * v[3];
+ }
+
+
+
+// Just do the rotation, not the translation... this is usually done with a 3x3
+// Matrix.
+__inline void m3dRotateVector(M3DVector3f vOut, const M3DVector3f p, const M3DMatrix33f m)
+ {
+ vOut[0] = m[0] * p[0] + m[3] * p[1] + m[6] * p[2];
+ vOut[1] = m[1] * p[0] + m[4] * p[1] + m[7] * p[2];
+ vOut[2] = m[2] * p[0] + m[5] * p[1] + m[8] * p[2];
+ }
+
+// Ditto above, but for doubles
+__inline void m3dRotateVector(M3DVector3d vOut, const M3DVector3d p, const M3DMatrix33d m)
+ {
+ vOut[0] = m[0] * p[0] + m[3] * p[1] + m[6] * p[2];
+ vOut[1] = m[1] * p[0] + m[4] * p[1] + m[7] * p[2];
+ vOut[2] = m[2] * p[0] + m[5] * p[1] + m[8] * p[2];
+ }
+
+
+// Scale a matrix (I don't beleive in Scaling matricies ;-)
+// Yes, it's faster to loop backwards... These could be
+// unrolled... but eh... if you find this is a bottleneck,
+// then you should unroll it yourself
+inline void m3dScaleMatrix33(M3DMatrix33f m, float scale)
+{ for(int i = 8; i >=0; i--) m[i] *= scale; }
+
+inline void m3dScaleMatrix33(M3DMatrix33d m, double scale)
+{ for(int i = 8; i >=0; i--) m[i] *= scale; }
+
+inline void m3dScaleMatrix44(M3DMatrix44f m, float scale)
+{ for(int i = 15; i >=0; i--) m[i] *= scale; }
+
+inline void m3dScaleMatrix44(M3DMatrix44d m, double scale)
+{ for(int i = 15; i >=0; i--) m[i] *= scale; }
+
+
+// Create a Rotation matrix
+// Implemented in math.cpp
+void m3dRotationMatrix33(M3DMatrix33f m, float angle, float x, float y, float z);
+void m3dRotationMatrix33(M3DMatrix33d m, double angle, double x, double y, double z);
+void m3dRotationMatrix44(M3DMatrix44f m, float angle, float x, float y, float z);
+void m3dRotationMatrix44(M3DMatrix44d m, double angle, double x, double y, double z);
+
+// Create a Translation matrix. Only 4x4 matrices have translation components
+inline void m3dTranslationMatrix44(M3DMatrix44f m, float x, float y, float z)
+{ m3dLoadIdentity44(m); m[12] = x; m[13] = y; m[14] = z; }
+
+inline void m3dTranslationMatrix44(M3DMatrix44d m, double x, double y, double z)
+{ m3dLoadIdentity44(m); m[12] = x; m[13] = y; m[14] = z; }
+
+
+// Translate matrix. Only 4x4 matrices supported
+inline void m3dTranslateMatrix44(M3DMatrix44f m, float x, float y, float z)
+{ m[12] += x; m[13] += y; m[14] += z; }
+
+inline void m3dTranslateMatrix44(M3DMatrix44d m, double x, double y, double z)
+{ m[12] += x; m[13] += y; m[14] += z; }
+
+
+// Scale matrix. Only 4x4 matrices supported
+inline void m3dScaleMatrix44(M3DMatrix44f m, float x, float y, float z)
+{ m[0] *= x; m[5] *= y; m[10] *= z; }
+
+inline void m3dScaleMatrix44(M3DMatrix44d m, double x, double y, double z)
+{ m[0] *= x; m[5] *= y; m[10] *= z; }
+
+
+// Transpose/Invert - Only 4x4 matricies supported
+#define TRANSPOSE44(dst, src) \
+{ \
+ for (int j = 0; j < 4; j++) \
+ { \
+ for (int i = 0; i < 4; i++) \
+ { \
+ dst[(j*4)+i] = src[(i*4)+j]; \
+ } \
+ } \
+}
+inline void m3dTransposeMatrix44(M3DMatrix44f dst, const M3DMatrix44f src)
+{ TRANSPOSE44(dst, src); }
+inline void m3dTransposeMatrix44(M3DMatrix44d dst, const M3DMatrix44d src)
+{ TRANSPOSE44(dst, src); }
+bool m3dInvertMatrix44(M3DMatrix44f dst, const M3DMatrix44f src);
+bool m3dInvertMatrix44(M3DMatrix44d dst, const M3DMatrix44d src);
+
+///////////////////////////////////////////////////////////////////////////////
+///////////////////////////////////////////////////////////////////////////////
+///////////////////////////////////////////////////////////////////////////////
+// Other Miscellaneous functions
+
+// Find a normal from three points
+// Implemented in math3d.cpp
+void m3dFindNormal(M3DVector3f result, const M3DVector3f point1, const M3DVector3f point2,
+ const M3DVector3f point3);
+void m3dFindNormal(M3DVector3d result, const M3DVector3d point1, const M3DVector3d point2,
+ const M3DVector3d point3);
+
+
+
+// Calculates the signed distance of a point to a plane
+inline float m3dGetDistanceToPlane(const M3DVector3f point, const M3DVector4f plane)
+ { return point[0]*plane[0] + point[1]*plane[1] + point[2]*plane[2] + plane[3]; }
+
+inline double m3dGetDistanceToPlane(const M3DVector3d point, const M3DVector4d plane)
+ { return point[0]*plane[0] + point[1]*plane[1] + point[2]*plane[2] + plane[3]; }
+
+
+// Get plane equation from three points and a normal
+void m3dGetPlaneEquation(M3DVector4f planeEq, const M3DVector3f p1, const M3DVector3f p2, const M3DVector3f p3);
+void m3dGetPlaneEquation(M3DVector4d planeEq, const M3DVector3d p1, const M3DVector3d p2, const M3DVector3d p3);
+
+// Determine if a ray intersects a sphere
+double m3dRaySphereTest(const M3DVector3d point, const M3DVector3d ray, const M3DVector3d sphereCenter, double sphereRadius);
+float m3dRaySphereTest(const M3DVector3f point, const M3DVector3f ray, const M3DVector3f sphereCenter, float sphereRadius);
+
+// Etc. etc.
+
+///////////////////////////////////////////////////////////////////////////////////////////////////////
+// Faster (and more robust) replacements for gluProject
+void m3dProjectXY( M3DVector2f vPointOut, const M3DMatrix44f mModelView, const M3DMatrix44f mProjection, const int iViewPort[4], const M3DVector3f vPointIn);
+void m3dProjectXYZ(M3DVector3f vPointOut, const M3DMatrix44f mModelView, const M3DMatrix44f mProjection, const int iViewPort[4], const M3DVector3f vPointIn);
+
+
+
+//////////////////////////////////////////////////////////////////////////////////////////////////
+// This function does a three dimensional Catmull-Rom "spline" interpolation between p1 and p2
+void m3dCatmullRom(M3DVector3f vOut, M3DVector3f vP0, M3DVector3f vP1, M3DVector3f vP2, M3DVector3f vP3, float t);
+void m3dCatmullRom(M3DVector3d vOut, M3DVector3d vP0, M3DVector3d vP1, M3DVector3d vP2, M3DVector3d vP3, double t);
+
+//////////////////////////////////////////////////////////////////////////////////////////////////
+// Compare floats and doubles...
+inline bool m3dCloseEnough(float fCandidate, float fCompare, float fEpsilon)
+ {
+ return (fabs(fCandidate - fCompare) < fEpsilon);
+ }
+
+inline bool m3dCloseEnough(double dCandidate, double dCompare, double dEpsilon)
+ {
+ return (fabs(dCandidate - dCompare) < dEpsilon);
+ }
+
+////////////////////////////////////////////////////////////////////////////
+// Used for normal mapping. Finds the tangent bases for a triangle...
+// Only a floating point implementation is provided.
+void m3dCalculateTangentBasis(const M3DVector3f pvTriangle[3], const M3DVector2f pvTexCoords[3], const M3DVector3f N, M3DVector3f vTangent);
+
+////////////////////////////////////////////////////////////////////////////
+// Smoothly step between 0 and 1 between edge1 and edge 2
+double m3dSmoothStep(double edge1, double edge2, double x);
+float m3dSmoothStep(float edge1, float edge2, float x);
+
+/////////////////////////////////////////////////////////////////////////////
+// Planar shadow Matrix
+void m3dMakePlanarShadowMatrix(M3DMatrix44d proj, const M3DVector4d planeEq, const M3DVector3d vLightPos);
+void m3dMakePlanarShadowMatrix(M3DMatrix44f proj, const M3DVector4f planeEq, const M3DVector3f vLightPos);
+
+double m3dClosestPointOnRay(M3DVector3d vPointOnRay, const M3DVector3d vRayOrigin, const M3DVector3d vUnitRayDir,
+ const M3DVector3d vPointInSpace);
+
+float m3dClosestPointOnRay(M3DVector3f vPointOnRay, const M3DVector3f vRayOrigin, const M3DVector3f vUnitRayDir,
+ const M3DVector3f vPointInSpace);
+
+#endif
+