קורס גרפיקה ממוחשבת 2010/2009 סמסטר א' Rendering 1 חלק מהשקפים מעובדים משקפים של פרדו דוראנד, טומס פנקהאוסר ודניאל כהן-אור

Transcription

1 קורס גרפיקה ממוחשבת 2010/2009 סמסטר א' Rendering 1 חלק מהשקפים מעובדים משקפים של פרדו דוראנד, טומס פנקהאוסר ודניאל כהן-אור

2 What is 3D rendering? Construct an image from a 3D model מצלמה תאורה View Plane Rendering מודל 3D 2

3 Rendering Scenarios אינטראקטיבי מייצרים תמונות בשבריר שנייה )לפחות 10 בשנייה( כאשר המשתמש שולט בפרמטרים של הרינדור יש צורך להשיג את האיכות הגבוהה ביותר בהתחשב בזמן הנתון )הקצב הנדרש( שימושי לויזואליזציות, משחקים וכו' 3

4 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' Jensen 4

5 3D Rendering Issues What does a 3D rendering system have to do? Camera Visible surface determination Lights Reflectance Shadows Indirect lllumination Sampling Etc. 5

6 Camera Models The most common model is pin-hole camera All captured light rays arrive along paths toward focal point without lens distortion (everything is in focus) Sensor response proportional to radiance Other models consider... Depth of field Motion blur Lens distortion View plane Eye position (focal point) aristotle

7 Camera Parameters Position Eye position (px, py, pz) Orientation View direction (dx, dy, dz) Up direction (ux, uy, uz) Aperature Field of view (xfov, yfov) Film plane Look at point View plane normal back right Up direction Eye Position View Plane Look at Point

8 3D Rendering Issues What does a 3D rendering system have to do? Camera Visible surface determination Lights Reflectance Shadows Indirect lllumination Sampling Etc. 8

9 Visible Surface Determination The color of each pixel on the view plane depends on the radiance emanating from visible surfaces Rays through view plane Simplest method is ray casting View plane Eye position

10 Ray Casting For each sample Construct ray from eye position through view plane Find first surface intersected by ray through pixel Compute color of sample based on surface radiance

11 Ray Casting For each sample Construct ray from eye position through view plane Find first surface intersected by ray through pixel Compute color of sample based on surface radiance

12 Ray Casting For each sample Construct ray from eye position through view plane Find first surface intersected by ray through pixel Compute color of sample based on surface radiance

13 3D Rendering Issues What does a 3D rendering system have to do? Camera Visible surface determination Lights Reflectance Shadows Indirect lllumination Sampling Etc. 13

14 Lights and Surfaces Different Lights 14

15 Different Materials Lights and Surfaces 15

16 Other Lighting Parameters Atmospheric attenuation Camera response 16

17 Lighting Simulation Lighting parameters Light source emission Surface reflectance Atmospheric attenuation Camera response Surface Light Source N N Camera

18 Lighting Simulation 18

19 Phong Reflectance Model Simple analytic model Diffuse reflection+ Specular reflection+ Emission+ ambient 19

20 3D Rendering Issues What does a 3D rendering system have to do? Camera Visible surface determination Lights Reflectance Shadows Indirect lllumination Sampling Etc. 20

21 Shadows Occlusions from light sources 21

22 Occlusions from light sources Soft shadows with area light source Shadows 22

23 Shadows 23

24 3D Rendering Issues What does a 3D rendering system have to do? Camera Visible surface determination Lights Reflectance Shadows Indirect lllumination Sampling Etc. 24

25 Path Types Direct diffuse + indirect specular and transmission 25

26 Path Types + Soft Shadows 26

27 Path Types + caustics 27

28 Path Types + indirect diffuse illumination 28

29 3D Rendering Issues What does a 3D rendering system have to do? Camera Visible surface determination Lights Reflectance Shadows Indirect lllumination Sampling Etc. 29

30 Scene can be sampled with any ray Rendering is a problem in sampling and reconstruction 30

31 Ray Casting 31

32 3D Rendering The color of each pixel on the view plane depends on the radiance emanating from visible surfaces Rays through view plane Eye position View plane

33 For each sample Construct ray from eye position through view plane Find first surface intersected by ray through pixel Compute color sample based on surface radiance Ray Casting

34 For each sample Construct ray from eye position through view plane Find first surface intersected by ray through pixel Compute color sample based on surface radiance Ray Casting Rays through view plane Eye position Samples on view plane

35 Simple implementation: Ray Casting Image RayCast(Camera 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 = ConstructRayThroughPixel(camera, i, j); Intersection hit = FindIntersection(ray, scene); image[i][j] = GetColor(hit); } } return image; }

36 Simple implementation: Ray Casting Image RayCast(Camera 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 = ConstructRayThroughPixel(camera, i, j); Intersection hit = FindIntersection(ray, scene); image[i][j] = GetColor(hit); } } return image; }

37 Constructing Ray Through a Pixel Up direction View Plane back P 0 right V Ray: P = P 0 + tv P

38 Constructing Ray Through a Pixel 2D Example P 1 Q = frustum half-angle d = distance to view plane right = towards x up P 1 = P 0 + d*towards - d*tan(q)*right P 2 = P 0 + d*towards + d*tan(q)*right P 0 right Q towards V d P P 2 2*d*tan(Q) P = P 1 + (i/width + 0.5) * 2*d*tan (Q)*right V = (P - P 0 ) / P - P 0 width width i -, 2 2 Ray: P = P 0 + tv

39 Simple implementation: Ray Casting Image RayCast(Camera 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 = ConstructRayThroughPixel(camera, i, j); Intersection hit = FindIntersection(ray, scene); image[i][j] = GetColor(hit); } } return image; }

40 Ray-Scene Intersection Intersections with geometric primitives Sphere Triangle Groups of primitives (scene) Acceleration techniques Bounding volume hierarchies Spatial partitions Uniform grids Octrees BSP trees

41 Ray-Sphere Intersection Ray: P = P 0 + tv Sphere: P - O 2 - r 2 = 0 P P V r P 0 O

42 Ray-Sphere Intersection I Ray: P = P 0 + tv Sphere: P - O 2 - r 2 = 0 Substituting for P, we get: P 0 + tv - O 2 - r 2 = 0 Algebraic Method Solve quadratic equation: at 2 + bt + c = 0 where: a = 1 b = 2 V (P 0 - O) c = P 0 - O 2 - r 2 = 0 P 0 V P r O P P = P 0 + tv

43 Ray-Sphere Intersection II Ray: P = P 0 + tv Sphere: P - O 2 - r 2 = 0 Geometric Method L = O - P 0 t ca = L V if (t ca < 0) return 0 d 2 = L L - t ca 2 if (d 2 > r 2 ) return 0 t hc = sqrt(r 2 - d 2 ) t = t ca - t hc and t ca + t hc P 0 V t ca L P r t hc d r O P P = P 0 + tv

44 Ray-Sphere Intersection Need normal vector at intersection for lighting calculations N = (P - O) / P - O N V P r P 0 O

45 Ray-Scene Intersection Intersections with geometric primitives Sphere» Triangle Groups of primitives (scene) Acceleration techniques Bounding volume hierarchies Spatial partitions Uniform grids Octrees BSP trees

46 Ray-Triangle Intersection First, intersect ray with plane Then, check if point is inside triangle P V P 0

47 Algebraic Method Ray-Plane Intersection Ray: P = P 0 + tv Plane: N(P-P 0 )=0 P N + c = 0 Substituting for P, we get: (P 0 + tv) N + c = 0 Solution: t = -(P 0 N + c) / (V N) And the intersection at: P = P 0 + tv P N P 0 V P 0

48 Ray-Triangle Intersection I Check if point is inside triangle algebraically T 3 For each side of triangle V 1 = T 1 P 0 V 2 = T 2 P 0 N 1 = V 2 x V 1 Normalize N 1 if (P -P 0 ) N 1 < 0 return FALSE; end T 1 P V 1 N 1 T 2 V 2 P 0

49 Ray-Triangle Intersection II Check if point is inside triangle parametrically Compute a, b: P = a (T 2 -T 1 ) + b (T 3 -T 1 ) T 3 Check if point inside triangle. 0 a 1 and 0 b 1 a + b 1 T 1 b P V a T 2 P 0

50 Other Ray-Primitive Intersections Cone, cylinder, ellipsoid: Similar to sphere Box Intersect 3 front-facing planes, return closest Convex polygon Same as triangle (check point-in-polygon algebraically) Concave polygon Same plane intersection More complex point-in-polygon test Algorithms for 3D object intersection:

51 Ray-Scene Intersection Find intersection with front-most primitive in group Intersection FindIntersection(Ray ray, Scene scene) { min_t = infinity min_primitive = NULL For 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) } Brute Force! D A E B F C

52 Ray-Scene Intersection Intersections with geometric primitives Sphere Triangle Groups of primitives (scene)» Acceleration techniques Bounding volume hierarchies Spatial partitions Uniform grids Octrees BSP trees

53 Bounding Volumes Check for intersection with simple shape first If ray doesn t intersect bounding volume, then it doesn t intersect its contents

54 Bounding Volume Hierarchies I Build hierarchy of bounding volumes Bounding volume of interior node contains all children 3 E 1 1 D F 2 C 3 A B D E F A 2 C B

55 Bounding Volume Hierarchies Use hierarchy to accelerate ray intersections Intersect node contents only if hit bounding volume 1 3 E 1 D F 2 C 3 C A B D E F A 2 B

56 Bounding Volume Hierarchies III Sort hits & detect early termination FindIntersection(Ray ray, Node node) { // Find intersections with child node bounding volumes... // Sort intersections front to back... // Process intersections (checking for early termination) min_t = infinity; for each intersected child i { if (min_t < bv_t[i]) break; shape_t = FindIntersection(ray, child); if (shape_t < min_t) { min_t = shape_t;} } return min_t; }

57 Ray-Scene Intersection Intersections with geometric primitives Sphere Triangle Groups of primitives (scene)» Acceleration techniques Bounding volume hierarchies Spatial partitions Uniform grids Octrees BSP trees

58 Uniform Grid Construct uniform grid over scene Index primitives according to overlaps with grid cells E D F C A B

59 Trace rays through grid cells Fast Incremental Uniform Grid E D F Only check primitives in intersected grid cells Given an entry point into a cell and a vector, its easy to calculate exit point A C B

60 Potential problem: Uniform Grid How choose suitable grid resolution? Too little benefit if grid is too coarse D E F Too much cost if grid is too fine C A B

61 Octree A tree data structure used to partition three dimensional space A 2D version is called a Quadtree 61

62 Octree Construct adaptive grid over scene Recursively subdivide box-shaped cells into 8 octants Index primitives by overlaps with cells E Generally fewer cells D F C A B Quadtree

63 Octree Trace rays through neighbor cells Fewer cells More complex neighbor finding E Trade-off fewer cells for more expensive traversal D F C A B

64 Octree Very useful in computer graphics, used for Intersections Collisions Color quantization Surface reconstruction (meshing) 64

65 Binary Space Partition (BSP) Tree Recursively partition space by planes Every cell is a convex polyhedron 1 3 E D F C A 4 B 2

66 Binary Space Partition (BSP) Tree Simple recursive algorithms Example: point finding 1 P 3 E D F C A 4 B 2

67 Binary Space Partition (BSP) Tree Trace rays by recursion on tree BSP construction enables simple front-to-back traversal 1 P 3 E D F C A 4 B 2

68 Binary Space Partition (BSP) 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) }

69 Other Accelerations Screen space coherence Check last hit first Beam tracing Pencil tracing Cone tracing Memory coherence Large scenes Parallelism Ray casting is embarassingly parallelizable etc.

70 Summary Writing a simple ray casting renderer is easy Generate rays Intersection tests Lighting calculations What s next? Illumination