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Effects needed for Realism Computer Graphics (Soft) Shadows Reflections (Mirrors and Glossy) CSE 167 [Win 19], Lecture 15: Ray Tracing Transparency (Water, Glass) Ravi Ramamoorthi Interreflections (Color Bleeding)

  1. Effects needed for Realism Computer Graphics § (Soft) Shadows § Reflections (Mirrors and Glossy) CSE 167 [Win 19], Lecture 15: Ray Tracing § Transparency (Water, Glass) Ravi Ramamoorthi § Interreflections (Color Bleeding) http://viscomp.ucsd.edu/classes/cse167/wi19 § Complex Illumination (Natural, Area Light) § Realistic Materials (Velvet, Paints, Glass) § And many more Ray Tracing § Different Approach to Image Synthesis as compared to Hardware pipeline (OpenGL) § Pixel by Pixel instead of Object by Object § Easy to compute shadows/transparency/etc Image courtesy Paul Heckbert 1983 Outline Ray Tracing: History § History § Appel 68 § Basic Ray Casting (instead of rasterization) § Whitted 80 [recursive ray tracing] § Comparison to hardware scan conversion § Landmark in computer graphics § Lots of work on various geometric primitives § Shadows / Reflections (core algorithm) § Lots of work on accelerations § Ray-Surface Intersection § Current Research § Optimizations § Real-Time raytracing (historically, slow technique) § Ray tracing architecture § Current Research 1

  2. Ray Tracing History Ray Tracing History From SIGGRAPH 18 Outline in Code Image Raytrace (Camera cam, Scene scene, int width, int height) { Image image = new Image (width, height) ; for (int i = 0 ; i < height ; i++) for (int j = 0 ; j < width ; j++) { Ray ray = RayThruPixel (cam, i, j) ; Intersection hit = Intersect (ray, scene) ; image[i][j] = FindColor (hit) ; } return image ; } Real Photo: Instructor and Turner Whitted at SIGGRAPH 18 Outline Ray Casting § History Produce same images as with OpenGL § Visibility per pixel instead of Z-buffer § Basic Ray Casting (instead of rasterization) § Find nearest object by shooting rays into scene § Comparison to hardware scan conversion § Shade it as in standard OpenGL § Shadows / Reflections (core algorithm) § Ray-Surface Intersection § Optimizations § Current Research 2

  3. Ray Casting Comparison to hardware scan-line § Per-pixel evaluation, per-pixel rays (not scan-convert each object). On face of it, costly § But good for walkthroughs of extremely large models (amortize preprocessing, low complexity) Virtual Viewpoint § More complex shading, lighting effects possible Virtual Screen Objects Multiple intersections: Use closest one (as does OpenGL) Ray misses all objects: Pixel colored black Ray intersects object: shade using color, lights, materials Shadows Outline Light Source § History § Basic Ray Casting (instead of rasterization) § Comparison to hardware scan conversion § Shadows / Reflections (core algorithm) § Ray-Surface Intersection Virtual Viewpoint § Optimizations § Current Research Virtual Screen Objects Shadow ray to light is unblocked: object visible Shadow ray to light is blocked: object in shadow Shadows: Numerical Issues Mirror Reflections/Refractions � Numerical inaccuracy may cause intersection to be below surface (effect exaggerated in figure) � Causing surface to incorrectly shadow itself � Move a little towards light before shooting shadow ray Virtual Viewpoint Virtual Screen Objects Generate reflected ray in mirror direction, Get reflections and refractions of objects 3

  4. Recursive Ray Tracing Problems with Recursion For each pixel § Reflection rays may be traced forever § Trace Primary Eye Ray, find intersection § Trace Secondary Shadow Ray(s) to all light(s) § Generally, set maximum recursion depth § Color = Visible ? Illumination Model : 0 ; § Trace Reflected Ray § Color += reflectivity * Color of reflected ray § Same for transmitted rays (take refraction into account) Effects needed for Realism � (Soft) Shadows � Reflections (Mirrors and Glossy) � Transparency (Water, Glass) � Interreflections (Color Bleeding) � Complex Illumination (Natural, Area Light) � Realistic Materials (Velvet, Paints, Glass) Discussed in this lecture Not discussed but possible with distribution ray tracing Turner Whitted 1980 Hard (but not impossible) with ray tracing; radiosity methods Outline Ray/Object Intersections § History § Heart of Ray Tracer § One of the main initial research areas § Basic Ray Casting (instead of rasterization) § Optimized routines for wide variety of primitives § Comparison to hardware scan conversion § Various types of info § Shadows / Reflections (core algorithm) § Shadow rays: Intersection/No Intersection § Primary rays: Point of intersection, material, normals § Ray-Surface Intersection § Texture coordinates § Optimizations § Work out examples § Triangle, sphere, polygon, general implicit surface § Current Research 4

  5. Ray-Sphere Intersection Ray-Sphere Intersection       ≡ P = 0 + ≡ P = 0 + ray P P 1 t ray P P 1 t         C ) − r 2 = 0 C ) − r 2 = 0 sphere ≡ ( P − C ) i ( P − sphere ≡ ( P − C ) i ( P − Substitute    ≡ P = 0 + ray P P 1 t       C ) − r 2 = 0 sphere ≡ ( 0 + 1 t − 0 + 1 t − P P C ) i ( P P C Simplify          C ) − r 2 = 0 t 2 ( 1 ) + 2 t 0 − C ) + ( 0 − 0 − P 1 i P P 1 i ( P P C ) i ( P P 0 Ray-Sphere Intersection Ray-Sphere Intersection             C ) − r 2 = 0 t 2 ( 1 ) + 2 t 0 − C ) + ( 0 − 0 − P 1 i P P 1 i ( P P C ) i ( P ≡ P = 0 + ray P P 1 t § Intersection point: Solve quadratic equations for t § Normal (for sphere, this is same as coordinates in sphere frame of reference, useful other tasks) § 2 real positive roots: pick smaller root   P − C = normal   § Both roots same: tangent to sphere P − C § One positive, one negative root: ray origin inside sphere (pick + root) § Complex roots: no intersection (check discriminant of equation first) Ray-Triangle Intersection Ray-Triangle Intersection § One approach: Ray-Plane intersection, then § One approach: Ray-Plane intersection, then check if inside triangle B check if inside triangle B A A n = ( C − A ) × ( B − A ) n = ( C − A ) × ( B − A ) § Plane equation: § Plane equation: ( C − A ) × ( B − A ) ( C − A ) × ( B − A )     P i  A i  P i  A i  plane ≡ n − n = 0 plane ≡ n − n = 0 § Combine with ray equation: C C      A i  0 i  ≡ P = 0 + ray P P 1 t n − P n    t =  1 t ) i  A i  1 i  0 + n = P n ( P P n 5

  6. Ray inside Triangle Ray inside Triangle § Once intersect with plane, still need to find if in P = α A + β B + γ C B triangle A β α ≥ 0, β ≥ 0, γ ≥ 0 α α + β + γ = 1 P § Many possibilities for triangles, general polygons (point in polygon tests) γ § We find parametrically [barycentric coordinates]. Also C useful for other applications (texture mapping) P − A = β ( B − A ) + γ ( C − A ) B P = α A + β B + γ C A β 0 ≤ β ≤ 1 , 0 ≤ γ ≤ 1 α α ≥ 0, β ≥ 0, γ ≥ 0 P β + γ ≤ 1 α + β + γ = 1 γ C Other primitives Ray-Tracing Transformed Objects § Much early work in ray tracing focused on ray-primitive We have an optimized ray-sphere test intersection tests § But we want to ray trace an ellipsoid … Solution: Ellipsoid transforms sphere § Cones, cylinders, ellipsoids § Apply inverse transform to ray, use ray-sphere § Boxes (especially useful for bounding boxes) § Allows for instancing (traffic jam of cars) § General planar polygons Mathematical details worked out in class § Many more § Many references. For example, chapter in Glassner introduction to ray tracing (see me if interested) Transformed Objects Outline § Consider a general 4x4 transform M § History § Will need to implement matrix stacks like in OpenGL § Basic Ray Casting (instead of rasterization) § Apply inverse transform M -1 to ray § Comparison to hardware scan conversion § Locations stored and transform in homogeneous coordinates § Shadows / Reflections (core algorithm) § Vectors (ray directions) have homogeneous coordinate set to 0 [so there is no action because of translations] § Ray-Surface Intersection § Do standard ray-surface intersection as modified § Optimizations § Transform intersection back to actual coordinates § Current Research § Intersection point p transforms as Mp § Distance to intersection if used may need recalculation § Normals n transform as M -t n. Do all this before lighting 6

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