CSC 307 1.0 Graphics Programming Department of Statistics and Computer Science
Graphics Programming OpenGL 3D Drawing 2
3D Graphics Projections Getting 3D to 2D 3D scene 2D image 3
Projections Orthographic Projection Perspective Projection Orthographic Perspective 4
Orthographic Projections glortho ( double left, double right, double bottom, double top, double near, double far); Top Toward the viewport Left Right Bottom Viewing Volume Near Far 5
Perspective Projection gluperspective ( double angle, double aspect, double near, double far); aspect = w/h w Observer h map map zoom in zoom out 6
Draw a 3D Model Object Composition Polygon 3D Model 7
Object Composition Use Transformation glpushmatrix ( ); glpopmatrix ( ); Save the current transformation state and then restore it after some objects have been placed 8
The Matrix Stack Draw a car use transformation The car body and four wheeles Transformation state Wheele 4 Wheele 4 Wheele 3 Wheele 2 Wheele 1 The Car Body 9
Hidden Surface Removal Enable Depth Testing glenable (GL_DEPTH_TEST); Hidden Surface 10
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 11
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 12
Sierpinski Gasket (2D) Start with a triangle Connect bisectors of sides and remove central triangle Repeat Example : Gasket.cpp 13
Moving to 3D We can easily make the program threedimensional by using typedef Glfloat point3[3] glvertex3f glortho But that would not be very interesting Instead, we can start with a tetrahedron 14
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 15
Example After 4 interations 16
triangle code void triangle( point a, point b, point c) { // right-hand rule glbegin(gl_polygon); glvertex3fv(a); glvertex3fv(b); glvertex3fv(c); glend(); } 17
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)); } 18
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); } 19
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 20
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 21
Locating the camera Position and orient the camera three inputs Eye, at, and direction up Camera is on Model-View mode 22
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); 23
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(); 24