Introduction to Visualization and Computer Graphics


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1 Introduction to Visualization and Computer Graphics DH2320, Fall 2015 Prof. Dr. Tino Weinkauf Introduction to Visualization and Computer Graphics Visibility Shading
2 3D Rendering Geometric Model Color Perspective Visibility Local Illumination Smooth Shading Simple Shadows Global Illumination
3 Visibility Algorithms
4 Rasterization Two Rendering Pipelines Project all triangles to the screen Rasterize them (convert to pixels) Determine visibility Apply shading (compute color) Raytracing Iterate over all pixels Determine visible triangle Compute shading, color pixel next lecture
5 Triangle / Polygon Rasterization Observations Straight lines remain straight! Triangles mapped to triangles After Perspective Projection Polygons to polyogns
6 3D Scene Rasterization Visiblity preprocessing or during rasterization Projection Visibility Rasterization
7 Two main algorithms Painter s algorithm (old) Simple version Correct version zbuffer algorithm Rasterization Dominant realtime method today
8 Painter s Algorithm
9 Painters Algorithm Sort primitives backtofront Draw with overwrite Drawbacks Slowish Painter s Algorithm O(n log n) for n primitives Millions per second Wrong Not guaranteed to always work
10 Counter Example Correct Algorithm Need to cut primitives Several strategies Notable: BSP Algorithm in Quake Old graphics textbooks list many variants No need for us to go deeper
11 zbuffer Algorithm
12 Algorithm Store depth value for each pixel Initialize to MAX_FLOAT Rasterize all primitives zbuffer Algorithm Compute fragment depth & color Do not overwrite if fragment is farer away than the one stored the one in the buffer color depth
13 Advantages Extremely simple Discussion: zbuffer Versatile only primitive rasterization required Very fast GeForce 2 Ultra: 2GPixel /sec (release year: 2000) GeForce 700 GTX Titan: 35 GPixel / sec (release year: 2013)
14 Disadvantages Extra memory required Discussion: zbuffer This was a serious in obstacle back then... Invented 39 years ago (1974; Catmull / Straßer) Only pixel resolution Need painter s algorithm for certain vector graphics computations No transparency This is a real problem for 3D games / interactive media Often fallback to sorting Solution: ABuffer, but no hardware support
15 Rasterization and Clipping
16 Rasterization How to rasterize Primitives? Two problems Rasterization Clipping color depth
17 Assumption Triangles only Triangle not outside screen No clipping required Rasterization
18 Several Algorithms... Triangle Rasterization
19 Example: two slabs Triangle Rasterization
20 Triangle Rasterization Δx constant precompute and add in each step Incremental rasterization
21 Incremental Rasterization Precompute steps in x, ydirection For boundary lines For linear interpolation within triangle Colors Texture coordinates (more later) Inner loop Only one addition ( DDA algorithm) Floating point value Strategies Fixedpoint arithmetics Bresenham / midpoint algorithm (requires if; problematic on modern CPUs)
22 Rasterization How to rasterize Primitives? Two problems Rasterization Clipping color depth
23 Why Clipping? Crashes write to offscreen memory!
24 Pixel Rejection if (x,y screen) continue; Clipping Strategies Can be arbitrarily slow (large triangles) Nope. Not a good idea. Screen space clipping Modify rasterizer to jump to visible pixels See tutorial 5 Efficient Still problems with when crossing camera plane (w = 0) a semigood idea
25 Smart Slab Renderer Does not crash, optimal complexity O(k) for k output fragments
26 Problem camera plane y 1 z 2 f z 1 y = f y z y 2 image plane Problem: Triangles crossing camera plane! Wrong results Need object space clipping
27 View Frustum Clipping near clipping plane far clipping plane four side planes six planes clip triangles against all six planes
28 Incremental Algorithm
29 Incremental Algorithm
30 Incremental Algorithm Output: Multiple Triangles
31 View Frustum Culling Further Optimization Complex shapes (whole bunnies) Coarse bounding volume (superset) Cube, Sphere Often: Axisaligned bounding box Reject all triangles inside if bounding volume outside view frustrum
32 3D Rendering Geometric Model Color Perspective Visibility Local Illumination Smooth Shading Simple Shadows Global Illumination
33 Shading Models
34 Reflectance Models mirror glossy surface diffuse surface
35 Interaction with Surfaces Viewer v n Light l object surface Local Shading Model Single point light source Shading model / material model Input: light vector l = pos light pos object Input: view vector v = pos camera pos object Input: surface normal n (orthogonal to surface) Output: color (RGB)
36 Interaction with Surfaces Viewer v n Light l object surface General scenario Multiple light sources? Light is linear Multiple light sources: add up contributions Double light strength double light output
37 Simplify notation Remark Define componentwise vector product x 1 y 1 x 1 y 1 x y = x 2 x 3 y 2 y 3 x 2 y 2 x 3 y 3 No fixed convention in literature The symbol only used in these lecture slides!
38 Lighting Calculations Remark Need to perform calculations for r, g, bchannels Often: output r = light r material r function v, l, n output g = light g material g function(v, l, n) output b = light b material b function(v, l, n) Shorter output = light_strength material function v, l, n
39 Shading effects Diffuse reflection Ambient reflection Perfect mirrors Glossy reflection Phong / BlinnPhong (Cook Torrance) Transparency & refraction Shading Effects
40 Shading effects Diffuse reflection Ambient reflection Perfect mirrors Glossy reflection Phong / BlinnPhong (Cook Torrance) Transparency & refraction Shading Effects
41 Diffuse ( Lambertian ) Surfaces n surface normal n θ n θ Equation (set to zero if negative) c ~ cos θ Less light received at flat angles c = c r c l cos θ light color surface color c intensity (scalar) c color (RGB, R 3 ) c r surface color (RGB) c l light color (RGB)
42 Diffuse ( Lambertian ) Surfaces n surface normal n θ n θ Equation c ~ cos θ Less light received at flat angles Attenuation: (point lights) 1 dist 2 c = c r c l cos θ 1 dist 2 light color surface color c intensity (scalar) c color (RGB, R 3 ) c r surface color (RGB) c l light color (RGB) 1 dist 2
43 Diffuse Reflection Diffuse Reflection Very rough surface microstructure Incoming light is scattered in all directions uniformly Diffuse surface (material) Lambertian surface (material)
44 Surface Normal? What is a surface normal? Tangent space: Plane approximation at a point x S Normal vector: Perpendicular to that plane Oriented surfaces: Pointing outwards (by convention) Orientation defined only for closed solids S tangent space surface normal n x R 3 point x
45 Triangles p 3 n p 2 Single Triangle Parametric equation p 1 + λ p 2 p 1 p 1 + μ p 3 p 1 λ, μ R Tangent space: the plane itself Normal vector p 2 p 1 p 3 p 1 Orientation convention: p 1, p 2, p 3 oriented counterclockwise Length: Any positive multiple works (often n = 1)
46 Triangle Meshes Smooth Triangle Meshes Store three different vertex normals E.g., from original surface (if known) Heuristic: Average neighboring triangle normals
47 Lambertian Surfaces n surface normal n θ n θ Equation c = c r c l cos θ = c r c l n, l n light direction normal vector (assuming: n = l = 1) θ l
48 Lambertian Bunny Face Normals Interpolated Normals
49 Shading effects Diffuse reflection Ambient reflection Perfect mirrors Glossy reflection Phong / BlinnPhong (Cook Torrance) Transparency & refraction Shading Effects
50 Ambient Reflection Problem Shadows are pure black Realistically, they should be gray Some light should bounce around... Solution: Add constant c = c a c a ambient light color surface color Not very realistic Need global light transport simulation for realistic results
51 Ambient Bunny Pure Lambertian Mixed with Ambient Light
52 Shading effects Diffuse reflection Ambient reflection Perfect mirrors Glossy reflection Phong / BlinnPhong (Cook Torrance) Transparency & refraction Shading Effects
53 Perfect Reflection Perfect Reflection Rays are perfectly reflected on surface Reflection about surface normal r = 2 n, l n l r n l
54 Perfect Reflection Difficult to compute Need to match camera and light emitter More later: Recursive raytracing Right image: Environment mapping Silver Bunny Reflective Bunny (Interpolated Normals)
55 Shading effects Diffuse reflection Ambient reflection Perfect mirrors Glossy reflection Phong / BlinnPhong (Cook Torrance) Transparency & refraction Shading Effects
56 Glossy Reflection Glossy Reflection Imperfect mirror Semirough surface Various models
57 Phong Illumination Model Traditional Model: Phong Model Physically incorrect (e.g.: energy conservation not guaranteed) But looks ok Always looks like plastic On the other hand, our world is full of plastic...
58 How does it work? Phong Model: Specular (glossy) part: (high) light color c = c p c l r r, v v cos r,v Ambient part: c = c r c a Diffuse part: c = c r c l n, l Add all terms together p 1,2 1 0,8 0,6 0,4 0,2 0 Phong Exponents p=1 p=2 p=5 p=10 p=50 p=100 v r n l
59 BlinnPhong BlinnPhong Model: Specular (glossy) part: c = c p c l h h, n n p v h n l cos h,n Halfangle direction h = 1 2 l l + v v In the plane: h h, n Approximation in 3D n = 1 2 r r, v v
60 Phong+Diffuse+Ambient Bunny BlinnPhong Bunny Interpolated Normals
61 Phong+Diffuse+Ambient Bunny BlinnPhong Bunny Interpolated Normals
62 Better Models Phong Bunny CookTorrance Model
63 Shading effects Diffuse reflection Ambient reflection Perfect mirrors Glossy reflection Phong / BlinnPhong (Cook Torrance) Transparency & refraction Shading Effects
64 Transparency Transparency Alphablending α = opacity Color + opacity: RGBα Blending Mix in α of front color, keep 1 α of back color % red, 50% green front back c = α c front + 1 α c back Not commutative! (order matters) unless monochrome
65 Refraction Materials of different index of refraction Refraction: Snell s Law Light rays change direction at interfaces Snell s Law sin θ 1 sin θ 2 = n 2 n 1 n 1, n 2 : indices of refraction vacuum: 1.0, air: water: 1.33, glass: θ 2 n θ 1 n n 1 n 2
66 Refraction Reflection Refraction Implementation (raytraced) Not a local shading model Global algorithms: mostly raytracing Various fake approximations for local shading
67 3D Rendering Geometric Model Color Perspective Visibility Local Illumination Smooth Shading Simple Shadows Global Illumination
68 Shading Algorithms
69 Flat Shading Flat Shading constant color per triangle
70 Flat Shading Gouraud Shading Algorithm compute color at vertices, interpolate color for pixels
71 Flat Shading Phong Shading Algorithm interpolate normals for each pixel
72 3D Rendering Geometric Model Color Global Illumination: next lecture Perspective Visibility Local Illumination Smooth Shading Simple Shadows Global Illumination
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