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// 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.
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// 160302: Added empty constructors for vec3 and vec4.
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// 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.
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// 2022-05-14: Corrected transposed version of lookAtv.
// 2023-01-31: Added shader upload utility functions.
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// 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!
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mat4 transpose(mat4 m)
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{
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;
}
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Rt = transpose(R); // Transpose = Invert -> felet ej i Transpose, och det �r en ortonormal matris
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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:
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| 0915175c |
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
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rot = SetMat4(u.x, u.y, u.z, 0,
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v.x, v.y, v.z, 0,
n.x, n.y, n.z, 0,
0, 0, 0, 1);
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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.
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// 2022: Yet another fix. Was it correct this time?
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mat4 perspective(float fovyInDegrees, float aspectRatio,
float znear, float zfar)
{
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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;
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}
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)
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matrix = transpose(matrix);
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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;
}
else
{
nanout = SetMat3(NAN, NAN, NAN,
NAN, NAN, NAN,
NAN, NAN, NAN);
out = nanout;
}
return out;
}
// Simple conversions
mat3 mat4tomat3(mat4 m)
{
mat3 result;
result.m[0] = m.m[0];
result.m[1] = m.m[1];
result.m[2] = m.m[2];
result.m[3] = m.m[4];
result.m[4] = m.m[5];
result.m[5] = m.m[6];
result.m[6] = m.m[8];
result.m[7] = m.m[9];
result.m[8] = m.m[10];
return result;
}
mat4 mat3tomat4(mat3 m)
{
mat4 result;
result.m[0] = m.m[0];
result.m[1] = m.m[1];
result.m[2] = m.m[2];
result.m[3] = 0;
result.m[4] = m.m[3];
result.m[5] = m.m[4];
result.m[6] = m.m[5];
result.m[7] = 0;
result.m[8] = m.m[6];
result.m[9] = m.m[7];
result.m[10] = m.m[8];
result.m[11] = 0;
result.m[12] = 0;
result.m[13] = 0;
result.m[14] = 0;
result.m[15] = 1;
return result;
}
vec3 vec4tovec3(vec4 v)
{
vec3 result;
result.x = v.x;
result.y = v.y;
result.z = v.z;
return result;
}
vec4 vec3tovec4(vec3 v)
{
vec4 result;
result.x = v.x;
result.y = v.y;
result.z = v.z;
result.w = 1;
return result;
}
// Stol... I mean adapted from glMatrix (WebGL math unit). Almost no
// changes despite changing language! But I just might replace it with
// a gaussian elimination some time.
mat4 InvertMat4(mat4 a)
{
mat4 b;
float c=a.m[0],d=a.m[1],e=a.m[2],g=a.m[3],
f=a.m[4],h=a.m[5],i=a.m[6],j=a.m[7],
k=a.m[8],l=a.m[9],o=a.m[10],m=a.m[11],
n=a.m[12],p=a.m[13],r=a.m[14],s=a.m[15],
A=c*h-d*f,
B=c*i-e*f,
t=c*j-g*f,
u=d*i-e*h,
v=d*j-g*h,
w=e*j-g*i,
x=k*p-l*n,
y=k*r-o*n,
z=k*s-m*n,
C=l*r-o*p,
D=l*s-m*p,
E=o*s-m*r,
q=1/(A*E-B*D+t*C+u*z-v*y+w*x);
b.m[0]=(h*E-i*D+j*C)*q;
b.m[1]=(-d*E+e*D-g*C)*q;
b.m[2]=(p*w-r*v+s*u)*q;
b.m[3]=(-l*w+o*v-m*u)*q;
b.m[4]=(-f*E+i*z-j*y)*q;
b.m[5]=(c*E-e*z+g*y)*q;
b.m[6]=(-n*w+r*t-s*B)*q;
b.m[7]=(k*w-o*t+m*B)*q;
b.m[8]=(f*D-h*z+j*x)*q;
b.m[9]=(-c*D+d*z-g*x)*q;
b.m[10]=(n*v-p*t+s*A)*q;
b.m[11]=(-k*v+l*t-m*A)*q;
b.m[12]=(-f*C+h*y-i*x)*q;
b.m[13]=(c*C-d*y+e*x)*q;
b.m[14]=(-n*u+p*B-r*A)*q;
b.m[15]=(k*u-l*B+o*A)*q;
return b;
};
// Two convenient printing functions suggested by Christian Luckey 2015.
// Added printMat3 2019.
void printMat4(mat4 m)
{
unsigned int i;
printf(" ---------------------------------------------------------------\n");
for (i = 0; i < 4; i++)
{
int n = i * 4;
printf("| %11.5f\t| %11.5f\t| %11.5f\t| %11.5f\t|\n",
m.m[n], m.m[n+1], m.m[n+2], m.m[n+3]);
}
printf(" ---------------------------------------------------------------\n");
}
void printMat3(mat3 m)
{
unsigned int i;
printf(" ---------------------------------------------------------------\n");
for (i = 0; i < 3; i++)
{
int n = i * 3;
printf("| %11.5f\t| %11.5f\t| %11.5f\t| \n",
m.m[n], m.m[n+1], m.m[n+2]);
}
printf(" ---------------------------------------------------------------\n");
}
void printVec3(vec3 in)
{
printf("(%f, %f, %f)\n", in.x, in.y, in.z);
}
|
| 0915175c |
/* Utility functions for easier uploads to shaders with error messages. */
// NEW as prototype 2022, added to VU 2023
#define NUM_ERRORS 8
static void ReportError(const char *caller, const char *name)
{
static unsigned int draw_error_counter = 0;
if(draw_error_counter < NUM_ERRORS)
{
fprintf(stderr, "%s warning: '%s' not found in shader!\n", caller, name);
draw_error_counter++;
}
else if(draw_error_counter == NUM_ERRORS)
{
fprintf(stderr, "%s: Number of errors bigger than %i. No more vill be printed.\n", caller, NUM_ERRORS);
draw_error_counter++;
}
}
void uploadMat4ToShader(GLuint shader, char *nameInShader, mat4 m)
{
if (nameInShader == NULL) return;
glUseProgram(shader);
GLint loc = glGetUniformLocation(shader, nameInShader);
if (loc >= 0)
glUniformMatrix4fv(loc, 1, GL_TRUE, m.m);
else
ReportError("uploadMat4ToShader", nameInShader);
}
void uploadUniformIntToShader(GLuint shader, char *nameInShader, GLint i)
{
if (nameInShader == NULL) return;
glUseProgram(shader);
GLint loc = glGetUniformLocation(shader, nameInShader);
if (loc >= 0)
glUniform1i(loc, i);
else
ReportError("uploadUniformIntToShader", nameInShader);
}
void uploadUniformFloatToShader(GLuint shader, char *nameInShader, GLfloat f)
{
if (nameInShader == NULL) return;
glUseProgram(shader);
GLint loc = glGetUniformLocation(shader, nameInShader);
if (loc >= 0)
glUniform1f(loc, f);
else
ReportError("uploadUniformFloatToShader", nameInShader);
}
void uploadUniformFloatArrayToShader(GLuint shader, char *nameInShader, GLfloat *f, int arrayLength)
{
if (nameInShader == NULL) return;
glUseProgram(shader);
GLint loc = glGetUniformLocation(shader, nameInShader);
if (loc >= 0)
glUniform1fv(loc, arrayLength, f);
else
ReportError("uploadUniformFloatToShader", nameInShader);
}
void uploadUniformVec3ToShader(GLuint shader, char *nameInShader, vec3 v)
{
if (nameInShader == NULL) return;
glUseProgram(shader);
GLint loc = glGetUniformLocation(shader, nameInShader);
if (loc >= 0)
glUniform3f(loc, v.x, v.y, v.z);
else
ReportError("uploadUniformVec3ToShader", nameInShader);
}
void uploadUniformVec3ArrayToShader(GLuint shader, char *nameInShader, vec3 *a, int arrayLength)
{
if (nameInShader == NULL) return;
glUseProgram(shader);
GLint loc = glGetUniformLocation(shader, nameInShader);
if (loc >= 0)
glUniform3fv(loc, arrayLength, (GLfloat *)a);
else
ReportError("uploadUniformVec3ArrayToShader", nameInShader);
}
void bindTextureToTextureUnit(GLuint tex, int unit)
{
glActiveTexture(GL_TEXTURE0 + unit);
glBindTexture(GL_TEXTURE_2D, tex);
}
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git.rcrnstn.net