OpenGL 3D Drawing
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This document discusses 3D graphics programming in OpenGL. It covers topics like projections, transformations, object composition, hidden surface removal, and drawing basic 3D objects like cubes and spheres. Code examples are provided to demonstrate drawing a 3D tetrahedral fractal using subdivision and the z-buffer algorithm for hidden surface removal. The document also discusses locating the camera using functions like gluLookAt and displaying a cube with different camera positions.
![14
Moving to 3D
•We can easily make the program three-
dimensional by using
typedef Glfloat point3[3]
glVertex3f
glOrtho
•But that would not be very interesting
•Instead, we can start with a tetrahedron
Budditha Hettige](https://image.slidesharecdn.com/3d-170814145011/85/OpenGL-3D-Drawing-14-320.jpg)
![15
3D Gasket
• We can subdivide each of the four faces
• We can easily make the program three-dimensional by using
typedef Glfloat point3[3]
glVertex3f
glOrtho
Budditha Hettige](https://image.slidesharecdn.com/3d-170814145011/85/OpenGL-3D-Drawing-15-320.jpg)
![18
subdivision code
void divide_triangle(point a, point b, point c,
int m)
{
point v1, v2, v3;
int j;
if(m>0)
{
for(j=0; j<3; j++) v1[j]=(a[j]+b[j])/2;
for(j=0; j<3; j++) v2[j]=(a[j]+c[j])/2;
for(j=0; j<3; j++) v3[j]=(b[j]+c[j])/2;
divide_triangle(a, v1, v2, m-1);
divide_triangle(c, v2, v3, m-1);
divide_triangle(b, v3, v1, m-1);
}
else(triangle(a,b,c));
}
Budditha Hettige](https://image.slidesharecdn.com/3d-170814145011/85/OpenGL-3D-Drawing-18-320.jpg)
![19
tetrahedron code
void tetrahedron( int m)
{
glColor3f(1.0,0.0,0.0);
divide_triangle(v[0], v[1], v[2], m);
glColor3f(0.0,1.0,0.0);
divide_triangle(v[3], v[2], v[1], m);
glColor3f(0.0,0.0,1.0);
divide_triangle(v[0], v[3], v[1], m);
glColor3f(0.0,0.0,0.0);
divide_triangle(v[0], v[2], v[3], m);
}
Budditha Hettige](https://image.slidesharecdn.com/3d-170814145011/85/OpenGL-3D-Drawing-19-320.jpg)
OpenGL 3D Drawing
- 1. CSC 307 1.0 Graphics Programming Budditha Hettige Department of Statistics and Computer Science
- 2. Graphics Programming OpenGL 3D Drawing 2Budditha Hettige
- 3. 3D Graphics • Projections – Getting 3D to 2D 3 3D scene 2D image Budditha Hettige
- 4. Projections • Orthographic Projection • Perspective Projection 4 Orthographic Perspective Budditha Hettige
- 5. Orthographic Projections • glOrtho ( double left, double right, double bottom, double top, double near, double far); 5 Toward the viewport Top Bottom Left Right Near Far Viewing Volume Budditha Hettige
- 6. Perspective Projection • gluPerspective ( double angle, double aspect, double near, double far); 6 zoom in zoom out map map Observer w h aspect = w/h Budditha Hettige
- 7. Draw a 3D Model • Object Composition 7 3D Model Polygon Budditha Hettige
- 8. Object Composition • Use Transformation – glPushMatrix ( ); – glPopMatrix ( ); – Save the current transformation state and then restore it after some objects have been placed Budditha Hettige 8
- 9. The Matrix Stack • Draw a car use transformation – The car body and four wheeles The Car Body Wheele 1 Wheele 2 Wheele 3 Wheele 4 Wheele 4 Transformation state Budditha Hettige 9
- 10. Hidden Surface Removal • Enable Depth Testing – glEnable (GL_DEPTH_TEST); 10 Hidden Surface Budditha Hettige
- 11. Drawing 3D Objects • Cube – void glutWireCube(GLdouble size); – void glutSolidCube(GLdouble size); • Sphere – void glutWireSphere(GLdouble radius, GLint slices, GLint stacks); – void glutSolidSphere(GLdouble radius, GLint slices, GLint stacks); • Cone 11Budditha Hettige
- 12. 12 Three-dimensional Applications •In OpenGL, two-dimensional applications are a special case of three-dimensional graphics –Not much changes –Use glVertex3*( ) –Have to worry about the order in which polygons are drawn or use hidden-surface removal –Polygons should be simple, convex, flat Budditha Hettige
- 13. 13 Sierpinski Gasket (2D) • Start with a triangle • Connect bisectors of sides and remove central triangle • Repeat • Example : Gasket.cpp Budditha Hettige
- 14. 14 Moving to 3D •We can easily make the program three- dimensional by using typedef Glfloat point3[3] glVertex3f glOrtho •But that would not be very interesting •Instead, we can start with a tetrahedron Budditha Hettige
- 15. 15 3D Gasket • We can subdivide each of the four faces • We can easily make the program three-dimensional by using typedef Glfloat point3[3] glVertex3f glOrtho Budditha Hettige
- 16. 16 Example After 4 interations Budditha Hettige
- 17. 17 triangle code void triangle( point a, point b, point c) {// right-hand rule glBegin(GL_POLYGON); glVertex3fv(a); glVertex3fv(b); glVertex3fv(c); glEnd(); } Budditha Hettige
- 18. 18 subdivision code void divide_triangle(point a, point b, point c, int m) { point v1, v2, v3; int j; if(m>0) { for(j=0; j<3; j++) v1[j]=(a[j]+b[j])/2; for(j=0; j<3; j++) v2[j]=(a[j]+c[j])/2; for(j=0; j<3; j++) v3[j]=(b[j]+c[j])/2; divide_triangle(a, v1, v2, m-1); divide_triangle(c, v2, v3, m-1); divide_triangle(b, v3, v1, m-1); } else(triangle(a,b,c)); } Budditha Hettige
- 19. 19 tetrahedron code void tetrahedron( int m) { glColor3f(1.0,0.0,0.0); divide_triangle(v[0], v[1], v[2], m); glColor3f(0.0,1.0,0.0); divide_triangle(v[3], v[2], v[1], m); glColor3f(0.0,0.0,1.0); divide_triangle(v[0], v[3], v[1], m); glColor3f(0.0,0.0,0.0); divide_triangle(v[0], v[2], v[3], m); } Budditha Hettige
- 20. 20 Problem • Because the triangles are drawn in the order they are defined in the program, the front triangles are not always rendered in front of triangles behind them get this want this Budditha Hettige
- 21. 21 Solution: Hidden-Surface Removal • We want to see only those surfaces in front of other surfaces • OpenGL uses a hidden-surface method called the z-buffer algorithm that saves depth information as objects are rendered so that only the front objects appear in the image Budditha Hettige
- 22. Locating the camera 22 Position and orient the camera – three inputs Eye, at, and direction – up Camera is on Model-View mode Budditha Hettige
- 23. Default Camera Settings • With default, camera is located at the origin and oriented at the negative z-axes • If place a cube at the origin, only one side of the cube is visible • Look at objects from different angles – Move the objects – Move the camera • Example – a cube • Glu function void gluLookAt(eyex, eyey, eyez, atx, aty, atz, upx, upy, upz) gluLookAt(1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0); 23Budditha Hettige
- 24. 24 Code: Display a cube void display() { glClear(GL_COLOR_BUFFER_BIT); glMatrixMode(GL_MODELVIEW); glLoadIdentity(); gluLookAt(1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0); glutWireCube(1.0f); glFlush(); } Budditha Hettige