deleted file mode 100755

@@ -1,1125 +0,0 @@

-// VectorUtils

-// Vector and matrix manipulation library for OpenGL, a package of the most essential functions.

-// Includes:

-// - Basic vector operations: Add, subtract, scale, dot product, cross product.

-// - Basic matrix operations: Multiply matrix to matrix, matric to vector, transpose.

-// - Creation of transformation matrixces: Translation, scaling, rotation.

-// - A few more special operations: Orthonormalizaton of a matrix, CrossMatrix,

-// - Replacements of some GLU functions: lookAt, frustum, perspective.

-// - Inverse and inverse transpose for creating normal matrices.

-// Supports both C and C++. The C interface makes it accessible from most languages if desired.

-

-// A note on completeness:

-// All operations may not be 100% symmetrical over all types, and some GLSL types are

-// missing (like vec2). These will be added if proven important. There is already

-// some calls of minor importance (mat3 * mat3, mat3 * vec3) included only for

-// symmetry. I don't want the code to grow a lot for such reasons, I want it to be

-// compact and to the point.

-

-// Current open design questions:

-// Naming conventions: Lower case or capitalized? (Frustum/frustum)

-// Prefix for function calls? (The cost would be more typing and making the code harder to read.)

-// Add vector operations for vec4? Other *essential* symmetry issues?

-// Names for functions when supporting both vec3 and vec4, mat3 and mat4? (vec3Add, vec4Add?)

-

-

-// History:

-

-// VectorUtils is a small (but growing) math unit by Ingemar Ragnemalm.

-// It originated as "geom3d" by Andrew Meggs, but that unit is no more

-// than inspiration today. The original VectorUtils(1) was based on it,

-// while VectorUtils2 was a rewrite primarily to get rid of the over-use

-// of arrays in the original.

-

-// New version 120201:

-// Defaults to matrices "by the book". Can also be configured to the flipped

-// column-wise matrices that old OpenGL required (and we all hated).

-// This is freshly implemented, limited testing, so there can be bugs.

-// But it seems to work just fine on my tests with translation, rotations

-// and matrix multiplications.

-

-// 1208??: Added lookAt, perspective, frustum

-// Also made Transpose do what it should. TransposeRotation is the old function.

-// 120913: Fixed perspective. Never trust other's code...

-// 120925: Transposing in CrossMatrix

-// 121119: Fixed one more glitch in perspective.

-

-// 130227 First draft to a version 3.

-// C++ operators if accessed from C++

-// Vectors by value when possible. Return values on the stack.

-// (Why was this not the case in VectorUtils2? Beause I tried to stay compatible

-// with an old C compiler. Older C code generally prefers all non-scalar data by

-// reference. But I'd like to move away from that now.)

-// Types conform with GLSL as much as possible (vec3, mat4)

-// Added some operations for mat3 and vec4, but most of them are more for

-// completeness than usefulness; I find vec3's and mat4's to be what I use

-// most of the time.

-// Also added InvertMat3 and InversTranspose to support creation of normal matrices.

-// Marked some calls for removal: CopyVector, TransposeRotation, CopyMatrix.

-// 130308: Added InvertMat4 and some more vec3/vec4 operators (+= etc)

-// 130922: Fixed a vital bug in CrossMatrix.

-// 130924: Fixed a bug in mat3tomat4.

-// 131014: Added TransposeMat3 (although I doubt its importance)

-// 140213: Corrected mat3tomat4. (Were did the correction in 130924 go?)

-// 151210: Added printMat4 and printVec3.

-// 160302: Added empty constructors for vec3 and vec4.

-// 170221: Uses _WIN32 instead of WIN32

-// 170331: Added stdio.h for printMat4 and printVec3

-// 180314: Added some #defines for moving closer to GLSL (dot, cross...).

-// 2021-05-15: Constructiors for vec3 etc replaced in order to avoid

-// problems with some C++ compilers.

-// 2022-05-14: Corrected transposed version of lookAtv.

-// 2023-01-31: Added shader upload utility functions.

-

-// You may use VectorUtils as you please. A reference to the origin is appreciated

-// but if you grab some snippets from it without reference... no problem.

-

-

-#include "VectorUtils3.h"

-

-// VS doesn't define NAN properly

-#ifdef _WIN32

-    #ifndef NAN

-        static const unsigned long __nan[2] = {0xffffffff, 0x7fffffff};

-        #define NAN (*(const float *) __nan)

-    #endif

-#endif

-

-char transposed = 0;

-

-	vec3 SetVector(GLfloat x, GLfloat y, GLfloat z)

-	{

-		vec3 v;

-		

-		v.x = x;

-		v.y = y;

-		v.z = z;

-		return v;

-	}

-

-// New better name

-	vec2 SetVec2(GLfloat x, GLfloat y)

-	{

-		vec2 v;

-		

-		v.x = x;

-		v.y = y;

-		return v;

-	}

-

-	vec3 SetVec3(GLfloat x, GLfloat y, GLfloat z)

-	{

-		vec3 v;

-		

-		v.x = x;

-		v.y = y;

-		v.z = z;

-		return v;

-	}

-

-	vec4 SetVec4(GLfloat x, GLfloat y, GLfloat z, GLfloat w)

-	{

-		vec4 v;

-		

-		v.x = x;

-		v.y = y;

-		v.z = z;

-		v.w = w;

-		return v;

-	}

-

-// Modern C doesn't need this, but Visual Studio insists on old-fashioned C and needs this.

-	mat3 SetMat3(GLfloat p0, GLfloat p1, GLfloat p2, GLfloat p3, GLfloat p4, GLfloat p5, GLfloat p6, GLfloat p7, GLfloat p8)

-	{

-		mat3 m;

-		m.m[0] = p0;

-		m.m[1] = p1;

-		m.m[2] = p2;

-		m.m[3] = p3;

-		m.m[4] = p4;

-		m.m[5] = p5;

-		m.m[6] = p6;

-		m.m[7] = p7;

-		m.m[8] = p8;

-		return m;

-	}

-

-// Like above; Modern C doesn't need this, but Visual Studio insists on old-fashioned C and needs this.

-	mat4 SetMat4(GLfloat p0, GLfloat p1, GLfloat p2, GLfloat p3,

-				GLfloat p4, GLfloat p5, GLfloat p6, GLfloat p7,

-				GLfloat p8, GLfloat p9, GLfloat p10, GLfloat p11, 

-				GLfloat p12, GLfloat p13, GLfloat p14, GLfloat p15

-				)

-	{

-		mat4 m;

-		m.m[0] = p0;

-		m.m[1] = p1;

-		m.m[2] = p2;

-		m.m[3] = p3;

-		m.m[4] = p4;

-		m.m[5] = p5;

-		m.m[6] = p6;

-		m.m[7] = p7;

-		m.m[8] = p8;

-		m.m[9] = p9;

-		m.m[10] = p10;

-		m.m[11] = p11;

-		m.m[12] = p12;

-		m.m[13] = p13;

-		m.m[14] = p14;

-		m.m[15] = p15;

-		return m;

-	}

-

-

-	// vec3 operations

-	// vec4 operations can easily be added but I havn't seen much need for them.

-	// Some are defined as C++ operators though.

-

-	vec3 VectorSub(vec3 a, vec3 b)

-	{

-		vec3 result;

-		

-		result.x = a.x - b.x;

-		result.y = a.y - b.y;

-		result.z = a.z - b.z;

-		return result;

-	}

-	

-	vec3 VectorAdd(vec3 a, vec3 b)

-	{

-		vec3 result;

-		

-		result.x = a.x + b.x;

-		result.y = a.y + b.y;

-		result.z = a.z + b.z;

-		return result;

-	}

-

-	vec3 CrossProduct(vec3 a, vec3 b)

-	{

-		vec3 result;

-

-		result.x = a.y*b.z - a.z*b.y;

-		result.y = a.z*b.x - a.x*b.z;

-		result.z = a.x*b.y - a.y*b.x;

-		

-		return result;

-	}

-

-	GLfloat DotProduct(vec3 a, vec3 b)

-	{

-		return a.x * b.x + a.y * b.y + a.z * b.z;

-	}

-

-	vec3 ScalarMult(vec3 a, GLfloat s)

-	{

-		vec3 result;

-		

-		result.x = a.x * s;

-		result.y = a.y * s;

-		result.z = a.z * s;

-		

-		return result;

-	}

-

-	GLfloat Norm(vec3 a)

-	{

-		GLfloat result;

-

-		result = (GLfloat)sqrt(a.x * a.x + a.y * a.y + a.z * a.z);

-		return result;

-	}

-

-	vec3 Normalize(vec3 a)

-	{

-		GLfloat norm;

-		vec3 result;

-

-		norm = (GLfloat)sqrt(a.x * a.x + a.y * a.y + a.z * a.z);

-		result.x = a.x / norm;

-		result.y = a.y / norm;

-		result.z = a.z / norm;

-		return result;

-	}

-

-	vec3 CalcNormalVector(vec3 a, vec3 b, vec3 c)

-	{

-		vec3 n;

-

-		n = CrossProduct(VectorSub(a, b), VectorSub(a, c));

-		n = ScalarMult(n, 1/Norm(n));

-		

-		return n;

-	}

-

-// Splits v into vn (parallell to n) and vp (perpendicular). Does not demand n to be normalized.

-	void SplitVector(vec3 v, vec3 n, vec3 *vn, vec3 *vp)

-	{

-		GLfloat nlen;

-		GLfloat nlen2;

-

-		nlen = DotProduct(v, n);

-		nlen2 = n.x*n.x+n.y*n.y+n.z*n.z; // Squared length

-		if (nlen2 == 0)

-		{

-			*vp = v;

-			*vn = SetVector(0, 0, 0);

-		}

-		else

-		{

-			*vn = ScalarMult(n, nlen/nlen2);

-			*vp = VectorSub(v, *vn);

-		}

-	}

-

-// Matrix operations primarily on 4x4 matrixes!

-// Row-wise by default but can be configured to column-wise (see SetTransposed)

-

-	mat4 IdentityMatrix()

-	{

-		mat4 m;

-		int i;

-

-		for (i = 0; i <= 15; i++)

-			m.m[i] = 0;

-		for (i = 0; i <= 3; i++)

-			m.m[i * 5] = 1; // 0,5,10,15

-		return m;

-	}

-

-	mat4 Rx(GLfloat a)

-	{

-		mat4 m;

-		m = IdentityMatrix();

-		m.m[5] = (GLfloat)cos(a);

-		if (transposed)

-			m.m[9] = (GLfloat)-sin(a);

-		else

-			m.m[9] = (GLfloat)sin(a);

-		m.m[6] = -m.m[9]; //sin(a);

-		m.m[10] = m.m[5]; //cos(a);

-		return m;

-	}

-

-	mat4 Ry(GLfloat a)

-	{

-		mat4 m;

-		m = IdentityMatrix();

-		m.m[0] = (GLfloat)cos(a);

-		if (transposed)

-			m.m[8] = (GLfloat)sin(a); // Was flipped

-		else

-			m.m[8] = (GLfloat)-sin(a);

-		m.m[2] = -m.m[8]; //sin(a);

-		m.m[10] = m.m[0]; //cos(a);

-		return m;

-	}

-

-	mat4 Rz(GLfloat a)

-	{

-		mat4 m;

-		m = IdentityMatrix();

-		m.m[0] = (GLfloat)cos(a);

-		if (transposed)

-			m.m[4] = (GLfloat)-sin(a);

-		else

-			m.m[4] = (GLfloat)sin(a);

-		m.m[1] = -m.m[4]; //sin(a);

-		m.m[5] = m.m[0]; //cos(a);

-		return m;

-	}

-

-	mat4 T(GLfloat tx, GLfloat ty, GLfloat tz)

-	{

-		mat4 m;

-		m = IdentityMatrix();

-		if (transposed)

-		{

-			m.m[12] = tx;

-			m.m[13] = ty;

-			m.m[14] = tz;

-		}

-		else

-		{

-			m.m[3] = tx;

-			m.m[7] = ty;

-			m.m[11] = tz;

-		}

-		return m;

-	}

-

-	mat4 S(GLfloat sx, GLfloat sy, GLfloat sz)

-	{

-		mat4 m;

-		m = IdentityMatrix();

-		m.m[0] = sx;

-		m.m[5] = sy;

-		m.m[10] = sz;

-		return m;

-	}

-

-	mat4 Mult(mat4 a, mat4 b) // m = a * b

-	{

-		mat4 m;

-

-		int x, y;

-		for (x = 0; x <= 3; x++)

-			for (y = 0; y <= 3; y++)

-				if (transposed)

-					m.m[x*4 + y] =	a.m[y+4*0] * b.m[0+4*x] +

-								a.m[y+4*1] * b.m[1+4*x] +

-								a.m[y+4*2] * b.m[2+4*x] +

-								a.m[y+4*3] * b.m[3+4*x];

-				else

-					m.m[y*4 + x] =	a.m[y*4+0] * b.m[0*4+x] +

-								a.m[y*4+1] * b.m[1*4+x] +

-								a.m[y*4+2] * b.m[2*4+x] +

-								a.m[y*4+3] * b.m[3*4+x];

-

-		return m;

-	}

-

-	// Ej testad!

-	mat3 MultMat3(mat3 a, mat3 b) // m = a * b

-	{

-		mat3 m;

-

-		int x, y;

-		for (x = 0; x <= 2; x++)

-			for (y = 0; y <= 2; y++)

-				if (transposed)

-					m.m[x*3 + y] =	a.m[y+3*0] * b.m[0+3*x] +

-								a.m[y+3*1] * b.m[1+3*x] +

-								a.m[y+3*2] * b.m[2+3*x];

-				else

-					m.m[y*3 + x] =	a.m[y*3+0] * b.m[0*3+x] +

-								a.m[y*3+1] * b.m[1*3+x] +

-								a.m[y*3+2] * b.m[2*3+x];

-

-		return m;

-	}

-

-	// mat4 * vec3

-	// The missing homogenous coordinate is implicitly set to 1.

-	vec3 MultVec3(mat4 a, vec3 b) // result = a * b

-	{

-		vec3 r;

-

-		if (!transposed)

-		{

-			r.x = a.m[0]*b.x + a.m[1]*b.y + a.m[2]*b.z + a.m[3];

-			r.y = a.m[4]*b.x + a.m[5]*b.y + a.m[6]*b.z + a.m[7];

-			r.z = a.m[8]*b.x + a.m[9]*b.y + a.m[10]*b.z + a.m[11];

-		}

-		else

-		{

-			r.x = a.m[0]*b.x + a.m[4]*b.y + a.m[8]*b.z + a.m[12];

-			r.y = a.m[1]*b.x + a.m[5]*b.y + a.m[9]*b.z + a.m[13];

-			r.z = a.m[2]*b.x + a.m[6]*b.y + a.m[10]*b.z + a.m[14];

-		}

-

-		return r;

-	}

-

-	// mat3 * vec3

-	vec3 MultMat3Vec3(mat3 a, vec3 b) // result = a * b

-	{

-		vec3 r;

-		

-		if (!transposed)

-		{

-			r.x = a.m[0]*b.x + a.m[1]*b.y + a.m[2]*b.z;

-			r.y = a.m[3]*b.x + a.m[4]*b.y + a.m[5]*b.z;

-			r.z = a.m[6]*b.x + a.m[7]*b.y + a.m[8]*b.z;

-		}

-		else

-		{

-			r.x = a.m[0]*b.x + a.m[3]*b.y + a.m[6]*b.z;

-			r.y = a.m[1]*b.x + a.m[4]*b.y + a.m[7]*b.z;

-			r.z = a.m[2]*b.x + a.m[5]*b.y + a.m[8]*b.z;

-		}

-		

-		return r;

-	}

-

-	// mat4 * vec4

-	vec4 MultVec4(mat4 a, vec4 b) // result = a * b

-	{

-		vec4 r;

-

-		if (!transposed)

-		{

-			r.x = a.m[0]*b.x + a.m[1]*b.y + a.m[2]*b.z + a.m[3]*b.w;

-			r.y = a.m[4]*b.x + a.m[5]*b.y + a.m[6]*b.z + a.m[7]*b.w;

-			r.z = a.m[8]*b.x + a.m[9]*b.y + a.m[10]*b.z + a.m[11]*b.w;

-			r.w = a.m[12]*b.x + a.m[13]*b.y + a.m[14]*b.z + a.m[15]*b.w;

-		}

-		else

-		{

-			r.x = a.m[0]*b.x + a.m[4]*b.y + a.m[8]*b.z + a.m[12]*b.w;

-			r.y = a.m[1]*b.x + a.m[5]*b.y + a.m[9]*b.z + a.m[13]*b.w;

-			r.z = a.m[2]*b.x + a.m[6]*b.y + a.m[10]*b.z + a.m[14]*b.w;

-			r.w = a.m[3]*b.x + a.m[7]*b.y + a.m[11]*b.z + a.m[15]*b.w;

-		}

-

-		return r;

-	}

-

-

-// Unnecessary

-// Will probably be removed

-//	void CopyMatrix(GLfloat *src, GLfloat *dest)

-//	{

-//		int i;

-//		for (i = 0; i <= 15; i++)

-//			dest[i] = src[i];

-//	}

-

-

-// Added for lab 3 (TSBK03)

-

-	// Orthonormalization of Matrix4D. Assumes rotation only, translation/projection ignored

-	void OrthoNormalizeMatrix(mat4 *R)

-	{

-		vec3 x, y, z;

-

-		if (transposed)

-		{

-			x = SetVector(R->m[0], R->m[1], R->m[2]);

-			y = SetVector(R->m[4], R->m[5], R->m[6]);

-//		SetVector(R[8], R[9], R[10], &z);

-			// Kryssa fram ur varandra

-			// Normera

-			z = CrossProduct(x, y);

-			z = Normalize(z);

-			x = Normalize(x);

-			y = CrossProduct(z, x);

-			R->m[0] = x.x;

-			R->m[1] = x.y;

-			R->m[2] = x.z;

-			R->m[4] = y.x;

-			R->m[5] = y.y;

-			R->m[6] = y.z;

-			R->m[8] = z.x;

-			R->m[9] = z.y;

-			R->m[10] = z.z;

-

-			R->m[3] = 0.0;

-			R->m[7] = 0.0;

-			R->m[11] = 0.0;

-			R->m[12] = 0.0;

-			R->m[13] = 0.0;

-			R->m[14] = 0.0;

-			R->m[15] = 1.0;

-		}

-		else

-		{

-		// NOT TESTED

-			x = SetVector(R->m[0], R->m[4], R->m[8]);

-			y = SetVector(R->m[1], R->m[5], R->m[9]);

-//		SetVector(R[2], R[6], R[10], &z);

-			// Kryssa fram ur varandra

-			// Normera

-			z = CrossProduct(x, y);

-			z = Normalize(z);

-			x = Normalize(x);

-			y = CrossProduct(z, x);

-			R->m[0] = x.x;

-			R->m[4] = x.y;

-			R->m[8] = x.z;

-			R->m[1] = y.x;

-			R->m[5] = y.y;

-			R->m[9] = y.z;

-			R->m[2] = z.x;

-			R->m[6] = z.y;

-			R->m[10] = z.z;

-

-			R->m[3] = 0.0;

-			R->m[7] = 0.0;

-			R->m[11] = 0.0;

-			R->m[12] = 0.0;

-			R->m[13] = 0.0;

-			R->m[14] = 0.0;

-			R->m[15] = 1.0;

-		}

-	}

-

-

-// Commented out since I plan to remove it if I can't see a good reason to keep it.

-//	// Only transposes rotation part.

-//	mat4 TransposeRotation(mat4 m)

-//	{

-//		mat4 a;

-//		

-//		a.m[0] = m.m[0]; a.m[4] = m.m[1]; a.m[8] = m.m[2];      a.m[12] = m.m[12];

-//		a.m[1] = m.m[4]; a.m[5] = m.m[5]; a.m[9] = m.m[6];      a.m[13] = m.m[13];

-//		a.m[2] = m.m[8]; a.m[6] = m.m[9]; a.m[10] = m.m[10];    a.m[14] = m.m[14];

-//		a.m[3] = m.m[3]; a.m[7] = m.m[7]; a.m[11] = m.m[11];    a.m[15] = m.m[15];

-//		

-//		return a;

-//	}

-

-	// Complete transpose!

-	mat4 transpose(mat4 m)

-	{

-		mat4 a;

-		

-		a.m[0] = m.m[0]; a.m[4] = m.m[1]; a.m[8] = m.m[2];      a.m[12] = m.m[3];

-		a.m[1] = m.m[4]; a.m[5] = m.m[5]; a.m[9] = m.m[6];      a.m[13] = m.m[7];

-		a.m[2] = m.m[8]; a.m[6] = m.m[9]; a.m[10] = m.m[10];    a.m[14] = m.m[11];

-		a.m[3] = m.m[12]; a.m[7] = m.m[13]; a.m[11] = m.m[14];    a.m[15] = m.m[15];

-		

-		return a;

-	}

-

-	// Complete transpose!

-	mat3 TransposeMat3(mat3 m)

-	{

-		mat3 a;

-		

-		a.m[0] = m.m[0]; a.m[3] = m.m[1]; a.m[6] = m.m[2];

-		a.m[1] = m.m[3]; a.m[4] = m.m[4]; a.m[7] = m.m[5];

-		a.m[2] = m.m[6]; a.m[5] = m.m[7]; a.m[8] = m.m[8];

-		

-		return a;

-	}

-

-// Rotation around arbitrary axis (rotation only)

-mat4 ArbRotate(vec3 axis, GLfloat fi)

-{

-	vec3 x, y, z;

-	mat4 R, Rt, Raxel, m;

-

-// Check if parallel to Z

-	if (axis.x < 0.0000001) // Below some small value

-	if (axis.x > -0.0000001)

-	if (axis.y < 0.0000001)

-	if (axis.y > -0.0000001)

-	{

-		if (axis.z > 0)

-		{

-			m = Rz(fi);

-			return m;

-		}

-		else

-		{

-			m = Rz(-fi);

-			return m;

-		}

-	}

-

-	x = Normalize(axis);

-	z = SetVector(0,0,1); // Temp z

-	y = Normalize(CrossProduct(z, x)); // y' = z^ x x'

-	z = CrossProduct(x, y); // z' = x x y

-

-	if (transposed)

-	{

-		R.m[0] = x.x; R.m[4] = x.y; R.m[8] = x.z;  R.m[12] = 0.0;

-		R.m[1] = y.x; R.m[5] = y.y; R.m[9] = y.z;  R.m[13] = 0.0;

-		R.m[2] = z.x; R.m[6] = z.y; R.m[10] = z.z;  R.m[14] = 0.0;

-

-		R.m[3] = 0.0; R.m[7] = 0.0; R.m[11] = 0.0;  R.m[15] = 1.0;

-	}

-	else

-	{

-		R.m[0] = x.x; R.m[1] = x.y; R.m[2] = x.z;  R.m[3] = 0.0;

-		R.m[4] = y.x; R.m[5] = y.y; R.m[6] = y.z;  R.m[7] = 0.0;

-		R.m[8] = z.x; R.m[9] = z.y; R.m[10] = z.z;  R.m[11] = 0.0;

-

-		R.m[12] = 0.0; R.m[13] = 0.0; R.m[14] = 0.0;  R.m[15] = 1.0;

-	}

-

-	Rt = transpose(R); // Transpose = Invert -> felet ej i Transpose, och det �r en ortonormal matris

-

-	Raxel = Rx(fi); // Rotate around x axis

-

-	// m := Rt * Rx * R

-	m = Mult(Mult(Rt, Raxel), R);

-	

-	return m;

-}

-

-

-// Not tested much

-mat4 CrossMatrix(vec3 a) // Matrix for cross product

-{

-	mat4 m;

-	

-	if (transposed)

-	{

-		m.m[0] =    0; m.m[4] =-a.z; m.m[8] = a.y; m.m[12] = 0.0;

-		m.m[1] = a.z; m.m[5] =    0; m.m[9] =-a.x; m.m[13] = 0.0;

-		m.m[2] =-a.y; m.m[6] = a.x; m.m[10]=    0; m.m[14] = 0.0;

-		m.m[3] =  0.0; m.m[7] =  0.0; m.m[11]=  0.0; m.m[15] = 0.0;

-		// NOTE! 0.0 in the homogous coordinate. Thus, the matrix can

-		// not be generally used, but is fine for matrix differentials

-	}

-	else

-	{

-		m.m[0] =    0; m.m[1] =-a.z; m.m[2] = a.y; m.m[3] = 0.0;

-		m.m[4] = a.z; m.m[5] =    0; m.m[6] =-a.x; m.m[7] = 0.0;

-		m.m[8] =-a.y; m.m[9] = a.x; m.m[10]=    0; m.m[11] = 0.0;

-		m.m[12] =  0.0; m.m[13] =  0.0; m.m[14]=  0.0; m.m[15] = 0.0;

-		// NOTE! 0.0 in the homogous coordinate. Thus, the matrix can

-		// not be generally used, but is fine for matrix differentials

-	}

-	

-	return m;

-}

-

-mat4 MatrixAdd(mat4 a, mat4 b)

-{

-	mat4 dest;

-	

-	int i;

-	for (i = 0; i < 16; i++)

-		dest.m[i] = a.m[i] + b.m[i];

-	

-	return dest;

-}

-

-

-void SetTransposed(char t)

-{

-	transposed = t;

-}

-

-

-// Build standard matrices

-

-mat4 lookAtv(vec3 p, vec3 l, vec3 v)

-{

-	vec3 n, u;

-	mat4 rot, trans;

-

-	n = Normalize(VectorSub(p, l));

-	u = Normalize(CrossProduct(v, n));

-	v = CrossProduct(n, u);

-

-//	rot = {{ u.x, u.y, u.z, 0,

-//                      v.x, v.y, v.z, 0,

-//                      n.x, n.y, n.z, 0,

-//                      0,   0,   0,   1 }};

-// VS friendly version:

-	if (transposed)

-	rot = SetMat4(u.x, v.x, n.x, 0,

-                  u.y, v.y, n.y, 0,

-                  u.z, v.z, n.z, 0,

-                  0,   0,   0,   1);

-	else

-	rot = SetMat4(u.x, u.y, u.z, 0,

-                  v.x, v.y, v.z, 0,

-                  n.x, n.y, n.z, 0,

-                  0,   0,   0,   1);

-	trans = T(-p.x, -p.y, -p.z);

-	return Mult(rot, trans);

-}

-

-mat4 lookAt(GLfloat px, GLfloat py, GLfloat pz, 

-			GLfloat lx, GLfloat ly, GLfloat lz,

-			GLfloat vx, GLfloat vy, GLfloat vz)

-{

-	vec3 p, l, v;

-	

-	p = SetVector(px, py, pz);

-	l = SetVector(lx, ly, lz);

-	v = SetVector(vx, vy, vz);

-	

-	return lookAtv(p, l, v);

-}

-

-// From http://www.opengl.org/wiki/GluPerspective_code

-// Changed names and parameter order to conform with VU style

-// Rewritten 120913 because it was all wrong...

-

-// Creates a projection matrix like gluPerspective or glFrustum.

-// Upload to your shader as usual.

-// 2022: Yet another fix. Was it correct this time?

-mat4 perspective(float fovyInDegrees, float aspectRatio,

-                      float znear, float zfar)

-{

-	float f = 1.0/tan(fovyInDegrees * M_PI / 360.0);

-	mat4 m = SetMat4(f/aspectRatio, 0, 0, 0,

-					0, f, 0, 0,

-					0, 0, (zfar+znear)/(znear-zfar), 2*zfar*znear/(znear-zfar),

-					0, 0, -1, 0);

-	if (transposed)

-		m = transpose(m);

-	return m;

-}

-

-mat4 frustum(float left, float right, float bottom, float top,

-                  float znear, float zfar)

-{

-    float temp, temp2, temp3, temp4;

-    mat4 matrix;

-    

-    temp = 2.0f * znear;

-    temp2 = right - left;

-    temp3 = top - bottom;

-    temp4 = zfar - znear;

-    matrix.m[0] = temp / temp2; // 2*near/(right-left)

-    matrix.m[1] = 0.0;

-    matrix.m[2] = 0.0;

-    matrix.m[3] = 0.0;

-    matrix.m[4] = 0.0;

-    matrix.m[5] = temp / temp3; // 2*near/(top - bottom)

-    matrix.m[6] = 0.0;

-    matrix.m[7] = 0.0;

-    matrix.m[8] = (right + left) / temp2; // A = r+l / r-l

-    matrix.m[9] = (top + bottom) / temp3; // B = t+b / t-b

-    matrix.m[10] = (-zfar - znear) / temp4; // C = -(f+n) / f-n

-    matrix.m[11] = -1.0;

-    matrix.m[12] = 0.0;

-    matrix.m[13] = 0.0;

-    matrix.m[14] = (-temp * zfar) / temp4; // D = -2fn / f-n

-    matrix.m[15] = 0.0;

-    

-    if (!transposed)

-    	matrix = transpose(matrix);

-    

-    return matrix;

-}

-

-// Not tested!

-mat4 ortho(GLfloat left, GLfloat right, GLfloat bottom, GLfloat top, GLfloat near, GLfloat far)

-{

-        float a = 2.0f / (right - left);

-        float b = 2.0f / (top - bottom);

-        float c = -2.0f / (far - near);

-

-        float tx = - (right + left)/(right - left);

-        float ty = - (top + bottom)/(top - bottom);

-        float tz = - (far + near)/(far - near);

-

-        mat4 o = SetMat4(

-            a, 0, 0, tx,

-            0, b, 0, ty,

-            0, 0, c, tz,

-            0, 0, 0, 1);

-        return o;

-}

-

-// The code below is based on code from:

-// http://www.dr-lex.be/random/matrix_inv.html

-

-// Inverts mat3 (row-wise matrix)

-// (For a more general inverse, try a gaussian elimination.)

-mat3 InvertMat3(mat3 in)

-{

-	float a11, a12, a13, a21, a22, a23, a31, a32, a33;

-	mat3 out, nanout;

-	float DET;

-	

-	// Copying to internal variables both clarify the code and

-	// buffers data so the output may be identical to the input!

-	a11 = in.m[0];

-	a12 = in.m[1];

-	a13 = in.m[2];

-	a21 = in.m[3];

-	a22 = in.m[4];

-	a23 = in.m[5];

-	a31 = in.m[6];

-	a32 = in.m[7];

-	a33 = in.m[8];

-	DET = a11*(a33*a22-a32*a23)-a21*(a33*a12-a32*a13)+a31*(a23*a12-a22*a13);

-	if (DET != 0)

-	{

-		out.m[0] = (a33*a22-a32*a23)/DET;

-		out.m[1] = -(a33*a12-a32*a13)/DET;

-		out.m[2] = (a23*a12-a22*a13)/DET;

-		out.m[3] = -(a33*a21-a31*a23)/DET;

-		out.m[4] = (a33*a11-a31*a13)/DET;

-		out.m[5] = -(a23*a11-a21*a13)/DET;

-		out.m[6] = (a32*a21-a31*a22)/DET;

-		out.m[7] = -(a32*a11-a31*a12)/DET;

-		out.m[8] = (a22*a11-a21*a12)/DET;

-	}

-	else

-	{

-		nanout = SetMat3(NAN, NAN, NAN,

-								NAN, NAN, NAN,

-								NAN, NAN, NAN);

-		out = nanout;

-	}

-	

-	return out;

-}

-

-// For making a normal matrix from a model-to-view matrix

-// Takes a mat4 in, ignores 4th row/column (should just be translations),

-// inverts as mat3 (row-wise matrix) and returns the transpose

-mat3 InverseTranspose(mat4 in)

-{

-	float a11, a12, a13, a21, a22, a23, a31, a32, a33;

-	mat3 out, nanout;

-	float DET;

-	

-	// Copying to internal variables

-	a11 = in.m[0];

-	a12 = in.m[1];

-	a13 = in.m[2];

-	a21 = in.m[4];

-	a22 = in.m[5];

-	a23 = in.m[6];

-	a31 = in.m[8];

-	a32 = in.m[9];

-	a33 = in.m[10];

-	DET = a11*(a33*a22-a32*a23)-a21*(a33*a12-a32*a13)+a31*(a23*a12-a22*a13);

-	if (DET != 0)

-	{

-		out.m[0] = (a33*a22-a32*a23)/DET;

-		out.m[3] = -(a33*a12-a32*a13)/DET;

-		out.m[6] = (a23*a12-a22*a13)/DET;

-		out.m[1] = -(a33*a21-a31*a23)/DET;

-		out.m[4] = (a33*a11-a31*a13)/DET;

-		out.m[7] = -(a23*a11-a21*a13)/DET;

-		out.m[2] = (a32*a21-a31*a22)/DET;

-		out.m[5] = -(a32*a11-a31*a12)/DET;

-		out.m[8] = (a22*a11-a21*a12)/DET;