Rendering. What is 3D rendering? קורס גרפיקה ממוחשבת 2008 סמסטר ב' מצלמה תאורה. Rendering Scenarios. Rendering Scenarios. 3D Rendering Issues

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1 What is rendering? onstruct an image from a model קורס גרפיקה ממוחשבת 008 סמסטר ב' מצלמה תאורה iew lane Rendering Rendering מודל חלק מהשקפים מעובדים משקפים של פרדו דוראנד, טומס פנקהאוסר ודניאל כהן-אור Rendering Scenarios אצווה )batch( כל תמונה מיוצרת ברמת פירוט גבוהה ככל האפשר עבור סט ספציפי של פרמטרים לוקח כמה זמן שצריך שימושי לפוטוריאליזם, סרטים וכו' Rendering Scenarios אינטראקטיבי מייצרים תמונות בשבריר שנייה )לפחות 0 בשנייה( כאשר המשתמש שולט בפרמטרים של הרינדור יש צורך להשיג את האיכות הגבוהה ביותר בהתחשב בזמן הנתון )הקצב הנדרש( שימושי לויזואליזציות, משחקים וכו' Jensen amera Models The most common model is pin-hole camera ll captured light rays arrive along paths toward focal point without lens distortion (everything is in focus) Sensor response proportional to radiance Other models consider... epth of field Motion blur Lens distortion iew plane ye position (focal point) Rendering Issues What does a rendering system have to do? amera isible surface determination Lights Reflectance Shadows Indirect lllumination Sampling tc.

2 iew lane amera arameters osition ye position (px, py, pz) Orientation iew direction (dx, dy, dz) ye position iew plane Up direction (ux, uy, uz) perature ield of view (xfov, yfov) ilm plane Look at point iew plane normal back right Up direction ye osition iew lane Look at oint 8 isible Surface etermination The color of each pixel on the view plane depends on the radiance emanating from visible surfaces Simplest method is ray casting Rays through view plane iew plane Rendering Issues What does a rendering system have to do? amera isible surface determination Lights Reflectance Shadows Indirect lllumination Sampling tc. ye position 9 or each sample onstruct ray from eye position through view plane ind first surface intersected by ray through pixel ompute color of sample based on surface radiance or each sample onstruct ray from eye position through view plane ind first surface intersected by ray through pixel ompute color of sample based on surface radiance

3 Rendering Issues What does a rendering system have to do? amera isible surface determination Lights Reflectance Shadows Indirect lllumination Sampling tc. or each sample onstruct ray from eye position through view plane ind first surface intersected by ray through pixel ompute color of sample based on surface radiance Lighting Simulation Lighting Simulation Lighting parameters Light source emission Surface reflectance tmospheric attenuation amera response Surface Light Source N N amera 6 Rendering Issues What does a rendering system have to do? amera isible surface determination Lights Reflectance Shadows Indirect lllumination Sampling tc. OpenGL Reflectance Model Simple analytic model iffuse reflection+ Specular reflection+ mission+ ambient 8 7

4 Shadows Shadows Occlusions from light sources Soft shadows with area light source Occlusions from light sources 0 9 Rendering Issues Shadows What does a rendering system have to do? amera isible surface determination Lights Reflectance Shadows Indirect lllumination Sampling tc. ath Types + Soft Shadows ath Types irect diffuse + indirect specular and transmission

5 ath Types + indirect diffuse illumination ath Types + caustics 6 Rendering Issues Scene can be sampled with any ray Rendering is a problem in sampling and reconstruction What does a rendering system have to do? amera isible surface determination Lights Reflectance Shadows Indirect lllumination Sampling tc. 8 7 Rendering The color of each pixel on the view plane depends on the radiance emanating from visible surfaces RY STING Rays through view plane Simplest method is ray casting iew plane ye position 9

6 or each sample onstruct ray from eye position through view plane ind first surface intersected by ray through pixel ompute color sample based on surface radiance Rays through view plane or each sample onstruct ray from eye position through view plane ind first surface intersected by ray through pixel ompute color sample based on surface radiance ye position Samples on view plane Simple implementation: Image Rayast(amera camera, Scene scene, int width, int height) { Image image = new Image(width, height); for (int i = 0; i < width; i++) { for (int j = 0; j < height; j++) { Ray ray = onstructraythroughixel(camera, i, j); Intersection hit = indintersection(ray, scene); image[i][j] = Getolor(hit); return image; Simple implementation: Image Rayast(amera camera, Scene scene, int width, int height) { Image image = new Image(width, height); for (int i = 0; i < width; i++) { for (int j = 0; j < height; j++) { Ray ray = onstructraythroughixel(camera, i, j); Intersection hit = indintersection(ray, scene); image[i][j] = Getolor(hit); return image; onstructing Ray Through a ixel onstructing Ray Through a ixel xample Q = frustum half-angle d = distance to view plane Up direction iew lane right = towards x up = + d*towards - d*tan(q)*right = + d*towards + d*tan(q)*right right Q towards d *d*tan(q) back right Ray: = + t = + (i/width + 0.) * *d*tan (Q)*right = ( - ) / - Ray: = + t 6

7 Ray-Scene Intersection Intersections with geometric primitives Sphere Triangle Groups of primitives (scene) cceleration techniques ounding volume hierarchies Spatial partitions Uniform grids Octrees S trees Simple implementation: Image Rayast(amera camera, Scene scene, int width, int height) { Image image = new Image(width, height); for (int i = 0; i < width; i++) { for (int j = 0; j < height; j++) { Ray ray = onstructraythroughixel(camera, i, j); Intersection hit = indintersection(ray, scene); image[i][j] = Getolor(hit); return image; Ray-Sphere Intersection I Ray-Sphere Intersection Ray: = + t Sphere: - O - r = 0 Substituting for, we get: + t - O - r = 0 lgebraic Method Ray: = + t Sphere: - O - r = 0 Solve quadratic equation: at + bt + c = 0 where: a = b = ( - O) c = - O - r = 0 r O r O = + t Ray-Sphere Intersection Ray-Sphere Intersection II Need normal vector at intersection for lighting calculations Ray: = + t Sphere: - O - r = 0 L = O - Geometric Method N = ( - O) / - O t ca = L if (t ca < 0) return 0 N r O d = L L - t ca if (d > r ) return 0 t hc = sqrt(r - d ) t = t ca - t hc and t ca + t hc 0 t ca L r t hc d r O = + t 7

8 Ray-Triangle Intersection irst, intersect ray with plane Then, check if point is inside triangle Ray-Scene Intersection Intersections with geometric primitives Sphere» Triangle Groups of primitives (scene) cceleration techniques ounding volume hierarchies Spatial partitions Uniform grids Octrees S trees Ray-Triangle Intersection I heck if point is inside triangle algebraically or each side of triangle = T - = T - N = x Normalize N if ( - ) N < 0 return LS; end T T lgebraic Method Ray: = + t lane: N(- )=0 N + c = 0 Substituting for, we get: ( + t) N + c = 0 Solution: t = -( N + c) / ( N) nd the intersection at: = + t Ray-lane Intersection N T N Other Ray-rimitive Intersections one, cylinder, ellipsoid: Similar to sphere ox Intersect front-facing planes, return closest onvex polygon Same as triangle (check point-in-polygon algebraically) oncave polygon Same plane intersection More complex point-in-polygon test Ray-Triangle Intersection II heck if point is inside triangle parametrically ompute a, b: = a (T -T ) + b (T -T ) heck if point inside triangle. 0 a and 0 b a + b T b a T T lgorithms for object intersection: 8

9 Ray-Scene Intersection Intersections with geometric primitives Sphere Triangle Groups of primitives (scene)» cceleration techniques ounding volume hierarchies Spatial partitions Uniform grids Octrees S trees Intersection indintersection(ray ray, Scene scene) { min_t = infinity min_primitive = NULL or each primitive in scene { t = Intersect(ray, primitive); if (t < min_t) then min_primitive = primitive min_t = t return Intersection(min_t, min_primitive) Ray-Scene Intersection ind intersection with front-most primitive in group rute orce! ounding olume Hierarchies I ounding olumes uild hierarchy of bounding volumes ounding volume of interior node contains all children heck for intersection with simple shape first If ray doesn t intersect bounding volume, then it doesn t intersect its contents ounding olume Hierarchies III Sort hits & detect early termination indintersection(ray ray, Node node) { // ind intersections with child node bounding volumes... // Sort intersections front to back... // rocess intersections (checking for early termination) min_t = infinity; for each intersected child i { if (min_t < bv_t[i]) break; shape_t = indintersection(ray, child); if (shape_t < min_t) { min_t = shape_t; return min_t; ounding olume Hierarchies Use hierarchy to accelerate ray intersections Intersect node contents only if hit bounding volume 9

10 Uniform Grid onstruct uniform grid over scene Index primitives according to overlaps with grid cells Ray-Scene Intersection Intersections with geometric primitives Sphere Triangle Groups of primitives (scene)» cceleration techniques ounding volume hierarchies Spatial partitions Uniform grids Octrees S trees Uniform Grid Uniform Grid otential problem: How choose suitable grid resolution? Too little benefit if grid is too coarse Trace rays through grid cells ast Incremental Too much cost if grid is too fine Only check primitives in intersected grid cells Given an entry point into a cell and a vector, its easy to calculate exit point onstruct adaptive grid over scene Recursively subdivide box-shaped cells into 8 octants Index primitives by overlaps with cells Octree Octree tree data structure used to partition three dimensional space analog of Quadtrees () Generally fewer cells Quadtree 9 0

11 Octree Octree ery useful in computer graphics, used for Intersections ollisions olor quantization Surface reconstruction (meshing) Trace rays through neighbor cells ewer cells More complex neighbor finding Trade-off fewer cells for more expensive traversal 6 inary Space artition (S) Tree Simple recursive algorithms xample: point finding inary Space artition (S) Tree Recursively partition space by planes very cell is a convex polyhedron inary Space artition (S) Tree RayTreeIntersect(Ray ray, Node node, double min, double max) { if (Node is a leaf) return intersection of closest primitive in cell, or NULL if none else dist = distance of the ray point to split plane of node near_child = child of node that contains the origin of Ray far_child = other child of node if the interval to look is on near side return RayTreeIntersect(ray, near_child, min, max) else if the interval to look is on far side return RayTreeIntersect(ray, far_child, min, max) else if the interval to look is on both side if (RayTreeIntersect(ray, near_child, min, dist)) return ; else return RayTreeIntersect(ray, far_child, dist, max) inary Space artition (S) Tree Trace rays by recursion on tree S construction enables simple front-to-back traversal

12 Summary Writing a simple ray casting renderer is easy Generate rays Intersection tests Lighting calculations What next? Illumination Screen space coherence heck last hit first eam tracing encil tracing one tracing Memory coherence Large scenes arallelism Ray casting is embarassingly parallelizable etc. Other ccelerations