# CS 464 Review. Review of Computer Graphics for Final Exam

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1 CS 464 Review Review of Computer Graphics for Final Exam

2 Goal: Draw 3D Scenes on Display Device 3D Scene Abstract Model Framebuffer Matrix of Screen Pixels In Computer Graphics: If it looks right then it is right

3 Components of 3D Scene Model Components Coordinate System Geometry = Models of Objects Lights Camera Textures Materials transforms Common Attributes Coordinates = x,y,z Cartesian Colors = r, g,b = Red, Green, Blue

4 Framebuffer device for showing pictures. Framebuffer Matrix of Screen Pixels Core Features of Framebuffer Matrix of Pixels Pixels: 8 bits of Red,Green,Blue, Alpha for 32 bits per pixel. Fixed width Fixed height Coordinates go left right, top to bottom. clearbuffer(acolor); setpixel(x,y, acolor);

5 What are our challenges? How do we draw simple 2D primitives? Lines (x,y) Triangles (x,y) How do we draw simple 3D primitives? Lines (x,y,z) Triangles (x,y,z)

6 What are our challenges? How do we draw simple 2D primitives? Lines (x,y) rasterize between two points. Triangles (x,y) clip the triangle, then rasterize. How do we draw simple 3D primitives? Lines (x,y,z) Project from 3D to 2D then use 2D methods. Triangles (x,y,z) Project from 3D to 2D then use 2D methods. Projection: - Perspective Projection and Orthographic Projection

7 Simple 2D Scene: Lines Scene Definition A simple list of vertices L1 L2 L3 L={ } xb1,yb1,xe1,ye1, xb2,yb2,xe2,ye2,. xb6,yb6,xe6,ye6 L7 L4 L6 L5 Coordinate Space= Framebuffer

8 Coordinate Spaces Normalized Device Coordinates Framebuffer Matrix of Screen Pixels 0,0 319,0 0, ,239 Coordinate Transform: F x =W x, F y =W y -F ymax

9 What are our Challenges? Normalized Device Coordinates are very limited How do I move objects? How do I map objects to different coordinates? How can I look at a scene from any view position I would like?

10 What are our Challenges? Normalized Device Coordinates are very limited How do I move objects? Matrix Transform How do I map objects to different coordinates? Matrix Transform How can I look at a scene from any view position I would like? View Transformation

11 3D to 2d: Perspective Projection Provides foreshortening. Has much higher visual realism. What users expect. Very simple perspective projection. X = x/z Y = y/z

12 View Tranformation

13 Standard Sequence of Transforms Image credits:

14 Now Where are We? 3D Scene Abstract Model Framebuffer Matrix of Screen Pixels In Computer Graphics: If it looks right then it is right

15 What are our Challenges? How do we represent complex Geometry? How do we integrate Lighting? How do we select colors for the Geometry we want to draw? How do we handle overlapping Triangles?

16 What are our Challenges? How do we represent complex Geometry? Modeling = easiest method is to use Triangles. How do we integrate Lighting? Lighting Models = ambient, diffuse, specular(phong) How do we select colors for the Geometry we want to draw? Shading Models = flat, gouraud, phong Texture Mapping = select a color from an image. Materials = define colors of the triangles and assign directly. How do we handle overlapping Triangles? Painters algorithm Z-Buffer à the standard.

17 How do we implement solutions? How do we represent complex Geometry? Triangles = vertices, normals, faces indices, use Program to create large models. How do we integrate Lighting? Typically = we generate a light color for each vertex and save it for rasterization. How do we select colors for the Geometry we want to draw? Rasterization = when rasterizing, we pick the color from: Light value interpolate. Texture Map = interpolate texture coordinates. Materials = use a triangle specific color and interpolate its value with the lighting. How do we handle overlapping Triangles? Painters algorithm sort all triangles before rendering and draw back to front. Z-Buffer à For each screen pixel keep a Z value and overwrite the closer pixels.

18 So what can we do now? 3D Scene Abstract Model Framebuffer Matrix of Screen Pixels In Computer Graphics: If it looks right then it is right

19 So how do we implement this so it is FAST!

20 So how do we implement this so it is FAST! We Introduce the Graphics Pipeline gl.drawelements(gl.triangles, cubevertexindexbuffer.numitems, gl.unsigned_short, 0);

21 Graphics Pipeline: process to draw scene. General Pipeline Geometry Pipeline

22 What are our Challenges? How do we represent complex Geometry? Modeling = easiest method is to use Triangles. How do we integrate Lighting? Lighting Models = ambient, diffuse, specular(phong) How do we select colors for the Geometry we want to draw? Shading Models = flat, gouraud, phong Texture Mapping = select a color from an image. Materials = define colors of the triangles and assign directly. How do we handle overlapping Triangles? Painters algorithm Z-Buffer à the standard.

23 How do we represent Geometry? Modeling Collections of triangles defined by: Vertices, Edges, Faces, Normals A set of vertices, a set of triangle indices = bare minimum geometry. Normals are present for what purposes? How to create complex models? Create by hand Use a program = Maya or Blender Scan the real world = Lidar Scanner and post-process. Collections of photographs = photogrammetry. Complex Geometry à eventually all translated to triangles. NURBS Parametric Surfaces Subdivision Surfaces Implicit Surfaces Constructive Solid Geometry

24 Blender

25 Constructive Solid Geometry (CSG) Represent solid object as hierarchy of boolean operations Union Intersection Difference

26 How Do We Select Colors for Pixels? Assign Simple Materials = simply store an r,g,b color with each object or face. Shading Models à controls how colors are modified Flat Shading Gouraud Shading Phong Shading Texture/Image Maps Assign s,t texture coordinates to Vertices and interpolate. What are types of things we can use Image maps for? Procedural Textures Pixel = f(s,t) where f is a function à I = cos(theta)*sin(phi) Programmable Fragment Shaders Use programmable code to calculate pixel color = most powerful.

27 How do we introduce Lighting? Lighting Components Ambient = a general representation for the common light in the room. Diffuse = the light that reflects in all direction from a surface. Specular = the light that reflects differently based on the viewing angle. Lighting Models Ambient Lighting Model à Ia = Ka*Ia Diffuse Lighting Model à Id = Kd * Id*Dot(Idir, Normal) Phong Lighting Model à Is = Ks * Dot(2*(Dot(Idir,N)N Idir),Idir)^alpha*ls

28 How Deal With Overlapping 3D Triangles Painters Algorithm What is an example of this failing? Z Buffer Algorithm What is an example of this failing?

29 Color Spaces RGB = Red, Green, Blue CMYK = Cyan, Magenta, Yellow, Black HSV = Hue, Saturation, Value HSI = Hue Saturation, Intensity LAB = Luminance, A=green-red, B = blue-yellow

30 Simple Linear Interplation Linear interpolation à c = a + t*b : t is a parameter from 0 to 1.0 Bilinear Interpolation Trilinear Interpolation

31 Simple Vector Arithmetic Vector addition = simply addition of all vector terms. Vector multiplication = Cross product Vector Normalization Angle between two products = Dot Product

32 What are Affine Transformations? What do Affine Transforms Preserve?

33 What are Affine Transformations? What do Affine Transforms Preserve? Points, straight lines, parallel lines, planes. Is the Perspective Projection an Affine transform? Examples of Affine transforms: Translation Scaling Rotations Shears Our typical Matrix transformations.

34 So What Can We Do Now????????? You Tell Me

35 What Can t We Do Yet? Shadows Reflections Anti-aliasing Scene Graphs Binary Space Partitioning Advanced Lighting à Diffuse/Diffuse interaction Stereo Systems Ray tracing and volume tracing.

36 What Can t We Do Yet? Shadows --> Draw the Scene Twice. Reflections à Draw the Scene once for every reflective surface. Anti-aliasing à Over-render the scene and scale down. Scene Graphs à Organize complex Scenes with Trees. Binary Space Partitioning à Rapid advanced modeling. Advanced Lighting à Diffuse/Diffuse interaction Stereo Systems à Use Two Cameras. Ray tracing and volume tracing.

37 The End Work on your final projects Study for Exam Practice Exam Available on Thursday

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