Seminar 2. Tessellation & Interpolation. Pierre Moreau. EDAF80 Introduction to Computer Graphics

Size: px

Start display at page:

Download "Seminar 2. Tessellation & Interpolation. Pierre Moreau. EDAF80 Introduction to Computer Graphics"

Darcy Miller
5 years ago
Views:

1 EDAF80 Introduction to Computer Graphics Seminar 2 Tessellation & Interpolation Pierre Moreau 2018 Includes slides by Carl Johan Gribel, and Michael Dogget,

2 Today Tessellation Linear and cubic interpolation Assignment 2 Git

3 Tessellation Walkthrough: Quad 1. Setup vertex array 2. Setup index array (triangulate)

4 Quad: vertex array creation Create vertex array (e.g. 3x3 vertices) auto vertices = std::vector<glm::vec3>(9); Assign one vertex vertices[index] = glm::vec3(x,y,z);

5 Quad: vertex array setup Set vertices vertices[3].x = 0 vertices[3].y = 0.5 vertices[3].z = vertices[8].x = 1 vertices[8].y = 1 vertices[8].z = vertices[1].x = 0.5 vertices[1].y = 0 vertices[1].z = 0

6 Quad: Triangulation Create index array ( 2(3-1)(3-1) triangles ) auto indices = std::vector<glm::uvec3>(8); Define triangle (indices for three vertices) indices[index] = glm::vec3(x,y,z);

7 Quad: Triangulation Indices in counter- clockwise order (ccw) indices[1].x = 0; indices[1].y = 4; indices[1].z = 3; indices[0].x = 0; indices[0].y = 1; Backface culling is off by default Turn it on to improve performance! indices[0].z = 4;

8 Parametric surfaces

9 Parametric surface & tangent space Map surface from 2D:

10 Parametric surface & tangent space Map surface from 2D: tangent binormal

11 Parametric surface & tangent space Map surface from 2D: tangent binormal normal

12 Surface Circle ring

13 Surface Sphere

14 Sphere Surface t and b can be simplified since only direction is important t needs to be simplified, or it will be undefined for ϕ=0

15 Today Tessellation Linear and cubic interpolation Assignment 2

16 Linear interpolation (LERP) p i p(x) p i+1

17 Linear interpolation (LERP) Interpolate between p i and p i+1 for x = [0, 1] p(0) p(0.5) p(1)

18 Cubic interpolation Catmull-Rom spline p i p i+2 p i-1 p i+1

19 Cubic interpolation Interpolate between p i and p i+1 for x = [0, 1], using p i-1, p i, p i+1, p i+2 p(0) p i+2 p i-1 p(0.5) p(1)

20 Tension low high = tension, how sharply the curve bends at control points Keep within [0,1] Good initial value: 0.5

21 Today Tessellation Linear and cubic interpolation Assignment 2

22 Take a break :) Unity Real-Time Adam demo MD16 22

23 Assignment 2 1. Tessellate objects from parametric equation 2. Linear and cubic interpolation

24 Assignment 2: Tessellation Implement function bodies in parametric_shapes.cpp : parametric_shapes::createsphere(...);

25 Assignment 2: Tessellation Implement function bodies in parametric_shapes.cpp : parametric_shapes::createsphere(...); Hint Examine, in the same file: createcirclering(...); Note: check parameter definitions & ranges circle ring sphere

26 Assignment 2: Tessellation Debugging normals/vectors Colorize Use the Normals -shader to represent normals as RGB-values Inspect illumination Is illumination consistent with the location of the light source?

27 Normals shader on a sphere Map from [-1,1] to [0,1] (normal * 0.5) X axis (1,0,0) becomes (0.5,0.5,1) Y axis (-1,0,-1) is 0, 0.5, 0 halfway between X&Z is (1,0.5,1) +X axis (0.5,0.5,1) -X axis MD14 (0,0,0) (1,1,1) (0.5,0.5,0) 27

28 Keyboard Controls Shaders - Number keys : 1,2,3,4 1 White 2 Diffuse 3 Normals 4 Texture Coords MD16 28

29 Keyboard Controls Polygon mode Z key switches between Filled, Line, and Point Filled Line Point MD16 29

30 Assignment 2 2. Interpolation Implement linear and cubic interpolation Function bodies in interpolation.cpp: glm::vec3 evallerp(...); glm::vec3 evalcatmullrom(...); Test with just 2 (lerp) or 4 (cubic) points first Then set up cyclic path of >10 points; animate an object along the path using both functions Use catmull_rom_tension and use_linear variable Then control them in GUI

31 Assignment 2 2. Interpolation Implementation sketch (cubic): // Init: glm::vec3 cp[n]; // N control points float path_pos = 0.0f; float pos_velocity =... // Main loop: int i = floor(path_pos); // floor returns closest lower integer // use indices (e.g.) i, i+1, i+2, i+3 to retrieve control // points from cp[]. // make sure indices wrap: 0, 1 N-1, 0, 1 // run interpolation // update the animated object path_pos += pos_velocity; // step forward

32 Today Tessellation Linear and cubic interpolation Assignment 2

33 OpenGL - More information learnopengl.com In particular Hello Triangle Triangle Can also use Elgkarv computer lab Ask questions on Forum MD16 33

34 GIT INTRODUCTION 34

35 Version Control Systems What: General Keep track of all changes Ease collaboration on common code base Known systems: Git, Subversion (SVN), Mercurial, Perforce Git Major Version Control system today Started by Linus Torvald for the Linux kernel, in Apr First version in Dec. 2005, continuous development MD17 35

36 A Commit Commit: Atomic unit keeping track of changes Info stored: * ID of the parent commit * Name and of who created the commit * A message * The actual change: - + means addition - - means removal - no prefix means no change, just for context * some other information MD17 36

37 Creation and Population To create a Git repository inside a folder: run git init Create a commit containing changes from certain files: git commit -m write a commit message -- file1 file2 file3 Each commit identified by unique ID; current commit also available under the name HEAD View a specific commit: git show commitid or git show HEAD List commits in reverse chronological order: git log Create a new Git repository from an existing one: git clone repository_address MD17 37

38 Remotes: Basics Everything done so far: local to your computer A Git repository: collection of commits + some pointers A remote is a regular Git repository: can be located on Github, or another folder on your computer Retrieve updates from a remote using git pull : download the missing commits Update a remote using git push : upload missing commits MD17 38

39 Merging and Conflicts If two persons push changes to a common remote: * one can push * the other get error message; solution: 1. pull the latest version 2. handle any conflicts locally 3. push the new version In case of conflict, Git will tell you which files had conflicts MD17 39

40 Conflicts (cont.) You can open the files with conflicts manually (see example on the right) You can resolve the conflict by invoking git mergetool, which will run a merge helper tool you configured Once solved, do not forget to add the files with conflicts before committing <<<<<<< How the code looks like on the version where you are doing the merge. If you are pulling and got a conflict, this is how your code looks like How the code looks like in the most recent common ancestor ======= How the code looks like on the version which you are merging in. If you are pulling, this is how the code looks like on the remote. >>>>>>> Example: <<<<<<< int a = 1; // You decided to change the value of a int a = 0; // Initially, the code looked like this ======= int b = 0; // Your coworker decided to rename the var >>>>>>> MD17 40

41 Other Features Telling Git to ignore files/folders using the.gitignore file Save changes for later reuse with git stash Mark versions (or something else) using git tag git worktree for sharing Git objects between multiple copies of a repository Rewrite commit history using git rebase and other commands Forget changes: git reset HEAD file1 file2 file3 MD17 41

EDAF80 Introduction to Computer Graphics. Seminar 3. Shaders. Michael Doggett. Slides by Carl Johan Gribel,

EDAF80 Introduction to Computer Graphics Seminar 3 Shaders Michael Doggett 2017 Slides by Carl Johan Gribel, 2010-13 Today OpenGL Shader Language (GLSL) Shading theory Assignment 3: (you guessed it) writing