Matrix4 Inverse() const {
double Result[4][4];
float const* src; /* array of transpose source matrix */
double det, invDet; /* determinant */
// set src
src = Transposed().Pointer();
// computing
double subfactor01 = src[10] * src[15] - src[11] * src[14];
double subfactor23 = src[9] * src[15] - src[11] * src[13];
double subfactor45 = src[9] * src[14] - src[10] * src[13];
double subfactor67 = src[8] * src[15] - src[11] * src[12];
double subfactor89 = src[8] * src[14] - src[10] * src[12];
double subfactor1011 = src[8] * src[13] - src[9] * src[12];
Result[0][0] = subfactor01 * src[5] - subfactor23 * src[6] + subfactor45 * src[7];
Result[0][1] = -subfactor01 * src[4] + subfactor67 * src[6] - subfactor89 * src[7];
Result[0][2] = subfactor23 * src[4] - subfactor67 * src[5] + subfactor1011 * src[7];
Result[0][3] = -subfactor45 * src[4] + subfactor89 * src[5] - subfactor1011 * src[6];
Result[1][0] = -subfactor01 * src[1] + subfactor23 * src[2] - subfactor45 * src[3];
Result[1][1] = subfactor01 * src[0] - subfactor67 * src[2] + subfactor89 * src[3];
Result[1][2] = -subfactor23 * src[0] + subfactor67 * src[1] - subfactor1011 * src[3];
Result[1][3] = subfactor45 * src[0] - subfactor89 * src[1] + subfactor1011 * src[2];
// computing
subfactor01 = src[2] * src[7] - src[3] * src[6];
subfactor23 = src[1] * src[7] - src[3] * src[5];
subfactor45 = src[1] * src[6] - src[2] * src[5];
subfactor67 = src[0] * src[7] - src[3] * src[4];
subfactor89 = src[0] * src[6] - src[2] * src[4];
subfactor1011 = src[0] * src[5] - src[1] * src[4];
Result[2][0] = subfactor01 * src[13] - subfactor23 * src[14] + subfactor45 * src[15];
Result[2][1] = -subfactor01 * src[12] + subfactor67 * src[14] - subfactor89 * src[15];
Result[2][2] = subfactor23 * src[12] - subfactor67 * src[13] + subfactor1011 * src[15];
Result[2][3] = -subfactor45 * src[12] + subfactor89 * src[13] - subfactor1011 * src[14];
Result[3][0] = - subfactor01 * src[9] + subfactor23 * src[10] - subfactor45 * src[11];
Result[3][1] = subfactor01 * src[8] - subfactor67 * src[10] + subfactor89 * src[11];
Result[3][2] = - subfactor23 * src[8] + subfactor67 * src[9] - subfactor1011 * src[11];
Result[3][3] = subfactor45 * src[8] - subfactor89 * src[9] + subfactor1011 * src[10];
// to calculate final inverse matrix
det = Result[0][0] * src[0] + Result[0][1] * src[1] +
Result[0][2] * src[2] + Result[0][3] * src[3];
invDet = 1.0f / det;
Matrix4 inverse;
float* fmat = (float*) inverse.Pointer();
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 4; j++) {
fmat[i * 4 + j] = float(Result[i][j] * invDet);
}
}
return inverse;
}
CubeExample(void)
: cube_instr(make_cube.Instructions())
, cube_indices(make_cube.Indices())
, projection_matrix(prog)
, camera_matrix(prog)
{
// Set the vertex shader source and compile it
VertexShader vs;
vs.Source(
"#version 150\n"
"uniform mat4 ProjectionMatrix, CameraMatrix;"
"layout (std140) uniform ModelBlock {"
" mat4 ModelMatrices[36];"
"};"
"in vec4 Position;"
"out vec3 vertColor;"
"void main(void)"
"{"
" mat4 ModelMatrix = ModelMatrices[gl_InstanceID];"
" gl_Position = "
" ProjectionMatrix *"
" CameraMatrix *"
" ModelMatrix *"
" Position;"
" vertColor = abs(normalize((ModelMatrix*Position).yxz));"
"}"
).Compile();
// set the fragment shader source and compile it
FragmentShader fs;
fs.Source(
"#version 150\n"
"in vec3 vertColor;"
"out vec4 fragColor;"
"void main(void)"
"{"
" fragColor = vec4(vertColor, 1.0);"
"}"
).Compile();
// attach the shaders to the program
prog.AttachShader(vs);
prog.AttachShader(fs);
// link and use it
prog.Link().Use();
projection_matrix.BindTo("ProjectionMatrix");
camera_matrix.BindTo("CameraMatrix");
// bind the VAO for the cube
cube.Bind();
// bind the VBO for the cube vertices
verts.Bind(Buffer::Target::Array);
{
std::vector<GLfloat> data;
GLuint n_per_vertex = make_cube.Positions(data);
// upload the data
Buffer::Data(Buffer::Target::Array, data);
// setup the vertex attribs array for the vertices
(prog|"Position").Setup<GLfloat>(n_per_vertex).Enable();
}
// make the matrices
{
// 36 x 4x4 matrices
std::vector<GLfloat> matrix_data(36*16);
auto p = matrix_data.begin(), e = matrix_data.end();
Angle<GLfloat> angle, astep = Angle<GLfloat>::Degrees(10);
while(p != e)
{
GLfloat cx = Cos(angle);
GLfloat sx = Sin(angle);
auto matrix = Transposed(Mat4f(
Vec4f( cx, 0.0, -sx, 0.0),
Vec4f(0.0, 1.0, 0.0, 0.0),
Vec4f( sx, 0.0, cx, 0.0),
Vec4f(0.0, 0.0, 0.0, 1.0)
) * Mat4f(
Vec4f(1.0, 0.0, 0.0,12.0),
Vec4f(0.0, 1.0, 0.0, 0.0),
Vec4f(0.0, 0.0, 1.0, 0.0),
Vec4f(0.0, 0.0, 0.0, 1.0)
));
p = std::copy(
Data(matrix),
Data(matrix)+Size(matrix),
p
);
angle += astep;
}
UniformBlock model_block(prog, "ModelBlock");
model_block.Binding(0);
block_buf.Bind(Buffer::Target::Uniform);
Buffer::Data(
Buffer::Target::Uniform,
matrix_data,
BufferUsage::DynamicDraw
);
block_buf.BindBaseUniform(0);
}
//
gl.ClearColor(0.9f, 0.9f, 0.9f, 0.0f);
gl.ClearDepth(1.0f);
gl.Enable(Capability::DepthTest);
}
/**
* @glsymbols
* @glfunref{LoadMatrix}
*/
static void LoadMatrix(const Mat4d& matrix)
{
OGLPLUS_GLFUNC(LoadMatrixd)(Data(Transposed(matrix)));
OGLPLUS_VERIFY(OGLPLUS_ERROR_INFO(LoadMatrixd));
}
void Matrix::Transpose()
{
*this = Transposed();
}
