Parametric description

Transcription

1 Examples: surface of revolution Vase Torus Parametric description

2 Parameterization for a subdivision curve Modeling Polygonal meshes Graphics I

3 Faces Face based objects: Polygonal meshes OpenGL is based on drawing a sequence of faces Face=triangles/quads (mostly) Polygonal meshes are a good example (a sequence of faces) A sequence of faces opengl (many other APIs)

4 How can we generate this kind of objects? output of modeling techniques (parametric, implicit, procedural) Output of other software (MAYA, 3dS Max, ) Very popular: a part of new multimedia(mpeg4-), and a standard for Games How can we generate this kind of objects? Modeling By Hand 3d scanner /3d digitizer

5 Cyberware Whole Body Color 3D Scanner Polygonal Meshes Goal: describe 3D objects by using polygonal mesh A collections of polygons Polygonal meshes (skin)

6 how to represent meshes!? Better method Redundant information, flexiblity, rounding error

7 Vertex List Vertex list: locations of vertices o Geometric Face list: indices of the other two o Topological Traverse of Polygons Clockwise Counter clockwise Convention: traverse counter clockwise as seen from outside

8 Normal Vectors Shading process: determine how much light from a light source is scattered off the face Vertex normal versus face normal Flat versus smooth shading

9 Finding Normal Vector In the case of triangular faces P 0 P 1 P 2 When does the formula fail? Vertex List Vertex list: locations of vertices o Geometric Normal list (optional): direction of normal vectors o Orientation Face list: indices of the other two o Topological

10 Obj Format (Face list and Vertex list) is a standard way for meshes Obj format from Alias/wavefront Maya, poser, 3Ds Max, Obj Format Tetrahedron # Obj file format with ext.obj v v v v f f f f 2 4 3

11 A real example MD2 format Designed by id software for the game Quak2 for character models in Games Binary Triangular mesh No normal list Animation is included

12 Key frames Key frames: interpolation Abrupt change More frames in between are needed

13 Linear interpolation Texture Mapping Pasting a 2D object on 3D objects

14 Adding Details on Object Pattern Wood Marble Cheap method to add Realism

15 Example

16 Correspondence : 2D and 3D (x,y,z) Color at (x,y,z)= color at (u,v) in the texture space (image) Keep the texture coordinates Texture space Evaluate texture coordinated of the mesh for just one time and save them Texture coordinates (u,v) have been associated to each vertex of each face of the object in most 3D formats and graphics software including obj format. MD2 and OpenGL

17 Example Example

18 Example Enable texture mapping by calling glenable(gl_texture_2d) Load a texture( from an image) glbegin(gl-quads); gltexcoord2f(0.0,0.1);glvertex3f(1.0,2.0,2.2); gltexcoord2f(0.2,0.6);glvertex3f(1.2,3.0,1.5); gltexcoord2f(0.8,0.7);glvertex3f(2.0,4.0,2.0); gltexcoord2f(0.7,0.3);glvertex3f(3.0,3.0,1.0); glend(); Texture Coordinates in OBJ Format v v v v v v v v vt vt vt vt vt vt vt vt vn vn vn vn vn vn f 1/1/1 2/2/1 3/3/1 f 3/3/1 4/4/1 1/1/1 f 4/4/2 3/3/2 5/5/2 f 5/5/2 6/6/2 4/4/2 f 6/6/3 5/5/3 7/7/3 f 7/7/3 8/8/3 6/6/3 f 8/8/4 7/7/4 2/2/4 f 2/2/4 1/1/4 8/8/4 f 3/3/5 2/2/5 7/7/5 f 7/7/5 5/5/5 3/3/5 Introduction to Computer f 4/4/6 Graphics 6/6/6 8/8/6 f 8/8/6 1/1/6 4/4/6

19 Textures in MD2 Same textures for all the frames The general structure Face list and texture lists are fixed for all the frames Vertex list changes in frames textures Face list Vertices in all frames

20 Mesh processing Collapse: edge, vertex, face Split: edge, vertex, face Add: new vertices, faces