Computer Graphics CS 543 Lecture 4 (Part 1) Building 3D Models (Part - PowerPoint PPT Presentation

Computer Graphics CS 543 – Lecture 4 (Part 1) Building 3D Models (Part 1) Prof Emmanuel Agu Computer Science Dept. Worcester Polytechnic Institute (WPI)

Objectives  Introduce simple data structures for building polygonal models  Vertex lists  Edge lists  Deprecated OpenGL vertex arrays  Drawing 3D objects

3D Applications  2D: points have (x,y) coordinates  3D: points have (x,y,z) coordinates  In OpenGL, 2D graphics are special case of 3D graphics

Setting up 3D Applications  Programming 3D, not many changes from 2D Load representation of 3D object into data structure 1.  Note: Vertices stored as 3D points (x, y, z)  Use vec3, glUniform3f instead of vec2 Draw 3D object 2. Hidden surface removal: Correctly determine order 3. in which primitives (triangles, faces) are rendered (Blocked faces NOT drawn)

3D Coordinate Systems Tip: sweep fingers x ‐ y: thumb is z  Y Y + z x x + z Left hand coordinate system •Not used in this class and Right hand coordinate system •Not in OpenGL

Generating 3D Models: GLUT Models One way of generating 3D shapes is by using GLUT 3D models (Restrictive?)  Note: Simply make GLUT 3D calls in application program (Not shaders)  Two main categories of GLUT models:  Wireframe Models  Solid Models  Solid m odels W irefram e m odels

3D Modeling: GLUT Models  Basic Shapes Cone: glutWireCone( ), glutSolidCone( )  Sphere: glutWireSphere( ), glutSolidSphere( )  Cube: glutWireCube( ), glutSolidCube( )  Torus  More advanced shapes: Cone Newell Teapot: (symbolic)  Dodecahedron, Torus  Sphere

GLUT Models: glutwireTeapot( )  Famous Utah Teapot has become an unofficial computer graphics mascot glutWireTeapot(0.5) - Create teapot of size 0.5, center positioned at (0,0,0) Also glutSolidTeapot( ) You need to apply transformations to position, scale and rotate it

3D Modeling: GLUT Models  Glut functions under the hood  generate sequence of points that define a shape  centered at 0.0 Example: glutWireCone generates sequence of vertices, and faces defining cone  and connectivity Generated vertices and faces passed to OpenGL for rendering  glutWireCone generates OpenGL program sequence of vertices, and receives vertices, faces defining cone Faces and renders them

Polygonal Meshes  Modeling with GLUT shapes (cube, sphere, etc) too restrictive  Difficult to approach realism  Other (preferred) way is using polygonal meshes:  Collection of polygons, or faces, that form “skin” of object  More flexible  Represents complex surfaces better  Examples:  Human face  Animal structures  Furniture, etc

Polygonal Mesh Example Sm oothed Mesh Out w ith ( w irefram e) Shading ( later)

Polygonal Meshes  Meshes now standard in graphics  OpenGL Good at drawing polygons, triangles  Mesh = sequence of polygons forming thin skin around object   Simple meshes exact. (e.g barn)  Complex meshes approximate (e.g. human face)  Use shading technique later to smoothen

Meshes at Different Resolutions Original: 424,000 60,000 triangles 1000 triangles triangles (14%). (0.2%) (courtesy of Michael Garland and Data courtesy of Iris Development.)

Representing a Mesh v 5 e 2 v 6 e 3  Consider a mesh e 9 e 8 v 8 v 4 e 1 e 11 e 10 v 7 e 4 e 7 v 1 e 12 e 6 v 3 e 5 v 2  There are 8 vertices and 12 edges  5 interior polygons  6 interior (shared) edges (shown in orange)  Each vertex has a location v i = (x i y i z i )

Simple Representation  Define each polygon by (x,y,z) locations of its vertices  Leads to OpenGL code such as vertex[i] = vec3(x1, y1, z1); vertex[i+1] = vec3(x6, y6, z6); vertex[i+2] = vec3(x7, y7, z7); i+=3;  Inefficient and unstructured  Vertices shared by many polygons are declared multiple times  Consider deleting vertex, moving vertex to new location  Must search for all occurrences

Geometry vs Topology  Better data structures should separate geometry from topology  Geometry: (x,y,z) locations of the vertices  Topology: How vertices and edges are connected  Example: a polygon is an ordered list of vertices with an edge connecting successive pairs of vertices and the last to the first  Topology holds even if geometry changes (vertex moves)

Polygon Traversal Convention  Use the right ‐ hand rule = counter ‐ clockwise encirclement of outward ‐ pointing normal  OpenGL can treat inward and outward facing polygons differently  The order {v 1 , v 6 , v 7 } and {v 6 , v 7 , v 1 } are equivalent in that the same polygon will be rendered by OpenGL but the order {v 1 , v 7 , v 6 } is different 4  The first two describe outwardly facing 3 5 polygons 2 6 1

Vertex Lists  Vertex list: (x,y,z) of vertices (its geometry) are put in array  Use pointers from vertices into vertex list  Polygon list: vertices connected to each polygon (face) Example: x 1 y 1 z 1 v 1 ‐ Polygon P1 of x 2 y 2 z 2 mesh is connected P1 v 7 x 3 y 3 z 3 to vertices (v1,v7,v6) P2 v 6 x 4 y 4 z 4 P3 ‐ Vertex v7 coordinates x 5 y 5 z 5. P4 v 8 are (x7,y7,z7) x 6 y 6 z 6 P5 v 5 v 6 x 7 y 7 z 7 topology x 8 y 8 z 8 geometry

Shared Edges  Vertex lists draw filled polygons correctly  If each polygon is drawn by its edges, shared edges are drawn twice  Alternatively: Can store mesh by edge list

Edge List Simply draw each edges once E.g e1 connects v1 and v6 v 5 e 2 v 6 e 3 x 1 y 1 z 1 e 9 e1 v1 e 8 v 8 x 2 y 2 z 2 e2 v6 e 11 e 1 e 10 e3 x 3 y 3 z 3 v 7 e 4 e 7 e4 v 1 x 4 y 4 z 4 e 12 v 3 e5 e 6 x 5 y 5 z 5. e 5 e6 v 2 x 6 y 6 z 6 e7 x 7 y 7 z 7 e8 Note polygons are x 8 y 8 z 8 e9 not represented

Modeling a Cube • In 3D, declare vertices as (x,y,z) using point3 v[3] • Define global arrays for vertices and colors typedef vex3 point3 ; point3 vertices[] = {point3(-1.0,-1.0,-1.0), point3(1.0,-1.0,-1.0), point3(1.0,1.0,-1.0), point3(-1.0,1.0,-1.0), point3(-1.0,-1.0,1.0), point3(1.0,-1.0,1.0), point3(1.0,1.0,1.0), point3(-1.0,1.0,1.0)}; typedef vec3 color3; color3 colors[] = {color3(0.0,0.0,0.0), color3(1.0,0.0,0.0), color3(1.0,1.0,0.0), color(0.0,1.0,0.0), color3(0.0,0.0,1.0), color3(1.0,0.0,1.0), color3(1.0,1.0,1.0), color3(0.0,1.0,1.0});

References  Angel and Shreiner  Hill and Kelley, appendix 4