Computer Vision Pattern Recognition Lab Computer Graphics Chapter

Computer Vision & Pattern Recognition Lab. Computer Graphics Chapter 13 Three-Dimensional Object Representations Computer Vision & Pattern Recognition Lab.

3 D object modeling How to describe objects (tree, building, cloth, glass, … )? => no single method n n n 2021 -05 -19 Polygon mesh: most commonly used Spline surface Constructive solid geometry(union, intersection, difference) Procedural method(fractal) Computer Vision & Pattern Recognition Lab. 2

13. 1. Polyhedra n Polyhedra (Polygon mesh) n n n 2021 -05 -19 "A set of surface polygons that enclose the object interior” Most commonly used boundary representation for 3 D objects How to represent? => Criteria: space/time Computer Vision & Pattern Recognition Lab. 3

13. 1. Polyhedra (1) Explicit rep. n n n 2021 -05 -19 Each polygon is represented by a list of vertices Each vertex is represented by (x, y, z) coordinates Inefficient <= 1 vertex is shared by many meshes Computer Vision & Pattern Recognition Lab. 4

13. 1. Polyhedra (2) Pointers to vertex list n n 2021 -05 -19 Each vertex is stored just once => vertex list Polygon is defined by a list of vertex indices. Space saving It is difficult to find shared edges Computer Vision & Pattern Recognition Lab. 5

13. 1. Polyhedra (3) Pointers to edge list Vertex list, edge list n Polygon is defined by a list of edge indices n Shared edge information is included in edge list n Polygon is displayed by all edges n 2021 -05 -19 Computer Vision & Pattern Recognition Lab. 6

13. 2. Open. GL Polyhedra Functions n glut. Wire. Tetrahedron(); n glut. Solid. Tetrahedron(); n glut. Wire. Cube(); n glut. Solid. Cube(); n glut. Wire. Octahedron(); n glut. Solid. Octahedron(); n glut. Wire. Dodecahedron(); n glut. Solid. Dodecahedron(); 2021 -05 -19 Computer Vision & Pattern Recognition Lab. 7

13. 3. Curved Surfaces n 2021 -05 -19 Problem: How to represent this object? Computer Vision & Pattern Recognition Lab. 8

13. 3. Curved Surfaces n Polygon meshes are linear approximations to curved surfaces => Needs many polygons to achieve accuracy n Sol. : More compact rep. of smooth (higher than linear) curves (1) Non-parametric representation (예: x 2+y 2 -r 2=0) n n Quadric surfaces: sphere, ellipsoid, torus, paraboloid, hyperboloid Superquadrics (2) Parametric representation (예: n n n 2021 -05 -19 ) Hermite curves Bezier curves Spline curves Computer Vision & Pattern Recognition Lab. 9

Mathematical modeling Object explicit form implicit form parametric form 2 D Curve 3 D Curve Surface Curve modeling

Curve, Surface representations 양함수식 표현 explicit form 음함수식form 표현 parametric 매개변수식form 표현 implicit y b y x a x z y x Curve modeling

13. 6. Open. GL Quadric-Surface and Cubic-Surface Functions n glut. Wire. Sphere(r, n. Lon, n. Lat ); n glut. Solid. Sphere(r, n. Lon, n. Lat); n glut. Wire. Cone( , , , ); n glut. Solid. Cone( , , , ); n glut. Wire. Torus( , , , ); n glut. Solid. Torus( , , , ); n glu. Cylinder( , , , ); 2021 -05 -19 Computer Vision & Pattern Recognition Lab. 12