Visibilidade
MO603/MC930
Visibilidade
•
•
•
•
•
Algoritmos básicos de visibilidade
Algoritmo pintor
Z-buffer
Estilos de Shading
Ray-casting
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
Removendo superfícies ocultas
• 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
Painter’s 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
Sorting Objects by Depth
BA
BA
Z
G
R
B
B
A
Zmin
R1
R2
G
B
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 don’t 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
V
N1
N2
• Each polygon is either front-facing or back-facing
– A polygon is backfacing if its normal points away from the viewer,
– i.e. V•N >= 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 painter’s algorithms
– If object is convex, backface culling is a complete visibility algorithm!
• When it doesn’t work
– If objects are not closed, back faces might be visible
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
– Can’t 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
• Painter’s:
– 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 won’t 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 isn’t 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 <GL/gl.h>
• #include <GL/glu.h>
• #include <GL/glut.h>
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;
}
Resultado
Comentários
• Definir vetores normais para todos vértices: glutSolidSphere()
faz isso.
• Criar, posicionar e habilitar uma (ou mais) fontes de luz:
glLightfv(), glEnable(), glLight*()
• Ex: GLfloat light_position[] = { 1.0, 1.0, 1.0, 0.0 };
•
glLightfv(GL_LIGHT0, GL_POSITION, light_position);
• default: GL_POSITION é (0, 0, 1, 0), eixo-Z negativo
• Selecionar um modelo de iluminação: glLightModel*()
• Definir propriedades materiais para os objetos na cena
Lembre-se
• Voce pode usar valores defaults para alguns parâmetros, de
iluminação; outros devem ser modificados
• Não se esqueça de habilitar todas as luzes que pretende
usar e também habilitar o cálculo de iluminação
• Voce pode usar “display lists” para maximizar eficiência
quando é necessário mudar as condições de iluminação
Computing Z for Z-buffering
• How to compute Z at each point for z-buffering?
• Can we interpolate Z?
– Linear interpolation along edge, along span
– Not quite. World space Z does not interpolate linearly in image space
• But if we linearly interpolate image space Z, it works!
– Perspective transforms planes to planes
– Note that image space Z is a nonlinear function of world space Z