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The visibility problem What is the nearest surface seen at any point in the image? How would YOU solve this problem?

Removendo superfícies ocultas A B

while (1) { get_viewing_point_from_mouse_position(); glClear(GL_COLOR_BUFFER_BIT); draw_3d_object_B(); draw_3d_object_A(); }

Removendo superfícies ocultas while (1) { get_viewing_point_from_mouse_position(); glClear(GL_COLOR_BUFFER_BIT); draw_3d_object_A(); draw_3d_object_B(); }

Removendo superfícies ocultas B A

Image Space Visibility Algorithms

Painters Algorithm Sort objects by depth (Z) Loop over objects in back-to-front order Project to image scan convert: image[x,y] = shade(x,y)

Sorting Objects by Depth Z Z min A B A B A B Sorting Objects by Depth R B G R1 R2 B G

Painter´s Algorithm Strengths –Simplicity: draw objects one-at-a-time, scan convert each –Handles transparency well Drawbacks –Sorting can be expensive (slower than linear in the number of objects) –Clumsy when ordering is cyclic, because of need to split –Interpenetrating polygons need to be split, too –Hard to sort non-polygonal objects Sometimes no need to sort –If objects are arranged in a grid, e.g. triangles in a height field z(x,y), such as a triangulated terrain Who uses it? –Postscript interpreters –OpenGL, if you dont glEnable(GL_DEPTH_TEST);

Representando objetos por malhas triangulares Divide objeto em faces triangulares A junção de todas as faces forma a casca do objeto Triangulo = estrutura (P1, P2, P3) T1={P1,P2,P3}, T2={P2,P4,P3} T3={P2, P5, P6}, T4={P6, P1, P2}, … Objeto = T1, T2, T3, T4, …

Backface culling Each polygon is either front-facing or back-facing –A polygon is backfacing if its normal points away from the viewer, –i.e. VN >= 0 When it works –If object is closed, back faces are never visible so no need to render them –Easy way to eliminate half your polygons –Can be used with both z-buffer and painters algorithms –If object is convex, backface culling is a complete visibility algorithm! When it doesnt work –If objects are not closed, back faces might be visible V N1 N2

Z-Buffer Algorithm Initialization loop over all x,y zbuf[x,y] = infinity Drawing steps loop over all objects scan convert object (loop over x,y) if z(x,y) < zbuf[x,y] compute z of this object at this pixel & test zbuf[x,y] = z(x,y) update z-buffer image[x,y] = shade(x,y) update image (typically RGB)

Z-Buffer Algorithm Strengths –Simple, no sorting or splitting –Easy to mix polygons, spheres, other geometric primitives Drawbacks –Cant handle transparency well –Need good Z-buffer resolution or you get depth ordering artifacts In OpenGL, this resolution is controlled by choice of clipping planes and number of bits for depth Choose ratio of clipping plane depths (zfar/znear) to be as small as possible Who uses it? –OpenGL, if you glEnable(GL_DEPTH_TEST);

Usando o buffer de profundidade glutInitDisplayMode (GLUT_DEPTH |.... ); glEnable(GL_DEPTH_TEST);... while (1) { glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); get_viewing_point_from_mouse_position(); draw_3d_object_A(); draw_3d_object_B(); }

Ray Casting A very flexible visibility algorithm loop y loop x shoot ray from eye through pixel (x,y) into scene intersect with all surfaces, find first one the ray hits shade surface point to compute pixel (x,y)s color

Comparing visibility algorithms Painters: –Implementation: moderate to hard if sorting & splitting needed –Speed: fast if objects are pre-sorted, otherwise slow –Generality: sorting & splitting make it ill-suited for general 3-D rendering Z-buffer: –Implementation: moderate, it can be implemented in hardware –Speed: fast, unless depth complexity is high –Generality: good but wont do transparency Ray Casting: –Implementation: easy, but hard to make it run fast –Speed: slow if many objects: cost is O((#pixels)´(#objects)) –Generality: excellent, can even do CSG, transparency, shadows

Really Hard Visibility Problems Extremely high scene complexity –a building walkthrough (QUAKE)? –A fly-by of the Grand Canyon (or any outdoor scene!) Z-buffering requires drawing EVERY triangle for each image –Not feasible in real time Usually Z-buffering is combined with spatial data structures –BSP trees are common (similar concept to octrees) For really complex scenes, visibility isnt always enough –Objects WAY in the distance are too small to matter –Might as well approximate far-off objects with simpler primitives –This is called geometry simplification

Programa exemplo (esfera) #include

Programa exemplo (esfera) void init(void) { GLfloat mat_specular[] = { 1.0, 1.0, 1.0, 1.0 }; GLfloat mat_shininess[] = { 50.0 }; GLfloat light_position[] = { 1.0, 1.0, 1.0, 0.0 }; glClearColor (0.0, 0.0, 0.0, 0.0); glShadeModel (GL_SMOOTH); glMaterialfv(GL_FRONT, GL_SPECULAR, mat_specular); glMaterialfv(GL_FRONT, GL_SHININESS, mat_shininess); glLightfv(GL_LIGHT0, GL_POSITION, light_position); glEnable(GL_LIGHTING); glEnable(GL_LIGHT0); glEnable(GL_DEPTH_TEST); }

Programa exemplo (esfera) void display(void) { glClear (GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); glutSolidSphere (1.0, 20, 16); glFlush (); }

Programa exemplo (esfera) void reshape (int w, int h) { glViewport (0, 0, (GLsizei) w, (GLsizei) h); glMatrixMode (GL_PROJECTION); glLoadIdentity(); if (w <= h) glOrtho (-1.5, 1.5, -1.5*(GLfloat)h/(GLfloat)w, 1.5*(GLfloat)h/(GLfloat)w, -10.0, 10.0); else glOrtho (-1.5*(GLfloat)w/(GLfloat)h, 1.5*(GLfloat)w/(GLfloat)h, -1.5, 1.5, -10.0, 10.0); glMatrixMode(GL_MODELVIEW); glLoadIdentity(); }

Programa exemplo (esfera) int main(int argc, char** argv) { glutInit(&argc, argv); glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB | GLUT_DEPTH); glutInitWindowSize (500, 500); glutInitWindowPosition (100, 100); glutCreateWindow (argv[0]); init (); glutDisplayFunc(display); glutReshapeFunc(reshape); glutMainLoop(); return 0; }