This project, completed as part of the coursework at the Benemérita Universidad Autónoma de Puebla, focuses on rotating a 3D pyramid along the Y and Z axes using parallel rotation. The aim is to apply matrix transformations to rotate a 3D object in space, enhancing the understanding of 3D graphics and transformations.
Rotating a vertex in 3D space involves altering its components along the x, y, and z axes. This project specifically targets rotations around the Y and Z axes using parallel rotation techniques. The implementation uses matrix multiplication to perform the necessary transformations.
- Implement parallel rotation for a 3D pyramid using matrix transformations in OpenGL.
- Apply learned concepts to rotate the pyramid around the Y and Z axes.
- Develop an understanding of 3D rotations and their applications in computer graphics.
- Initialization: Set up the OpenGL environment and window properties.
- Rotation Functions: Implement functions for rotating the pyramid around the Y and Z axes.
- Matrix Operations: Utilize matrix multiplication for applying transformations.
- Animation Loop: Continuously apply rotations to animate the 3D pyramid.
The project includes the following main components:
This function sets up the OpenGL environment, defining the color of the window and the projection parameters.
void init(void) {
glClearColor(0.0, 0.0, 0.0, 1.0);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluPerspective(60, 1.0, 1.0, 30.0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glTranslatef(0.0, 0.0, -3.0);
}This function handles the parallel rotation of the pyramid along the specified axis. It first translates the pyramid, performs the rotation, and then translates it back.
void Operaciones3D::RotacionParalela(char eje, float theta, float distA, float distB) {
switch (eje) {
case 'X': // Parallel rotation around X-axis
translate(0, -distA, -distB);
rotateX(DegToRad(theta));
MultM(R, T, A);
translate(0, distA, distB);
MultM(T, A, A);
break;
case 'Y': // Parallel rotation around Y-axis
translate(0, -distA, -distB);
rotateY(DegToRad(theta));
MultM(R, T, A);
translate(0, distA, distB);
MultM(T, A, A);
break;
case 'Z': // Parallel rotation around Z-axis
translate(0, -distA, -distB);
rotateZ(DegToRad(theta));
MultM(R, T, A);
translate(0, distA, distB);
MultM(T, A, A);
break;
}
}This function applies a translation to the 3D object by modifying its coordinates.
void translate(float dx, float dy, float dz) {
float T[4][4] = {
{1, 0, 0, dx},
{0, 1, 0, dy},
{0, 0, 1, dz},
{0, 0, 0, 1}
};
MultM(R, T, A);
}These functions define the rotation matrices for the X, Y, and Z axes and multiply them with the transformation matrix.
void rotateX(float theta) {
float R[4][4] = {
{1, 0, 0, 0},
{0, cos(theta), -sin(theta), 0},
{0, sin(theta), cos(theta), 0},
{0, 0, 0, 1}
};
MultM(T, R, A);
}
void rotateY(float theta) {
float R[4][4] = {
{cos(theta), 0, sin(theta), 0},
{0, 1, 0, 0},
{-sin(theta), 0, cos(theta), 0},
{0, 0, 0, 1}
};
MultM(T, R, A);
}
void rotateZ(float theta) {
float R[4][4] = {
{cos(theta), -sin(theta), 0, 0},
{sin(theta), cos(theta), 0, 0},
{0, 0, 1, 0},
{0, 0, 0, 1}
};
MultM(T, R, A);
}This function multiplies two 4x4 matrices.
void MultM(float A[4][4], float B[4][4], float C[4][4]) {
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 4; j++) {
C[i][j] = 0;
for (int k = 0; k < 4; k++) {
C[i][j] += A[i][k] * B[k][j];
}
}
}
}The project initializes a graphical window and applies parallel rotations to the pyramid along the Y and Z axes. The rotation is continuous, providing a dynamic visual representation of the 3D transformations.
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