Concept of 3D Modeling

1. Concept of 3D Modeling • Model • The representation of the object or system • Modeling • The creation and manipulation of an object or system representation.

2. Issue • How to represent the “world”? • Efficiency to Modeler • Efficiency to Renderer

3. Model Types • Model -> Render -> Display • Types of Models: • Graphical model (geometric model) • Using geometric entities to describe the object, • Eg. Lines, polygons, curves , etc • Descriptive model • Mathematical or conceptual representation • Eg. Equations and attributes description.

4. Pmc*M = Pwc + + Model representation and modeling • Line / Curve / Curve / Polygon / Surface • Constructive solid-geometry and hierarchical modeling • Hierarchical modeling • The graphical model is composed by a number of individual models. • The modeling will involve the transformation process. • Transform individual local coordinate (model coordinates) to world coordinates. • The graphical object are constructed by transforming (eg. Translate, rotate) the local individual object from local coordinates to the world coordinates.

5. Model representation and modeling • Hierarchical modeling with structure • A hierarchical model can be created with structures by nesting the structures into one another to form a tree organization.

6. 3D Object Representation • Boundary Representation • Surface representation • Eg. Polygon facets, splines surfaces, which can be converted into polygon mesh.

7. 3D Object Representation • Solid representation (space-partitioning) • Represent the object by a set of small solids (eg. Cubes), so that the interior property is described (eg. Octree structure).

8. Vertices and Polygons Representation • All objects can be represented by: • A set of vertices (points) • A set of lines • A set of polygons

9. Vertex Representation • Point in a Frame • Possible Characteristics • Location (x,y,z) • Color • Normal Vector • Discussed Later

10. Polygon Representation • Polygon Data • Include geometric data and attribute data • Geometric Data : - Spatial Information (location) • Polygon List Edge List Vertex List • Attribute data : - Surface property • Eg. Texture property, transparency property , reflectance property

11. Polygon Data • Geometric data • ( Vertex – edge - polygon format) • Vertex list Edge list Polygon list structure structure structure Vertices Edges Polygons { { { V1: x1, y1, z1; e1: V1,V2; P1: e1,e2,e3 V2: x2, y2, z2; e2: V2, V3; P2: e2, e4, e5 … … ….. Vn: xn, yn, zn en: Vi, Vj PK: ei ,ej ,ek } } }

12. Object Representation – Vertices vs Polygons • Shared Vertices between Polygons • Cube Example

13. Polygon • Normally a convex polygon on a single plane • Possible Characteristics • Ordered Set of Vertices • Outward Facing Side (Normal) • Right Hand Rule about Vertex Order • Color • Transparency vs Opaque • Example: • Triangles, Squares, Rectangles, Irregular Polygons

14. Objects • Surfaces Only • Composed of Polygons (Facets)

15. Shared Vertices • Each facet (polygon) is a set of vertices • Adjacent polygons share vertices • A single vertex is common between adjacent polygons Shared Vertex

16. Object and Object Hierarchies • Additional Properties • Animation or Behavior • Objects can be made up of Objects • Sub-objects may have independent properties

17. Normals • Normal is a vector perpendicular to the surface at a given point

18. The normal is the same for a flat surface The normal is different at different points on a curved surface Normals (Contiued)

19. Polygon Normals • Normal Characteristics: • Indicates “outward face” • Magnitude is irrelevant so often the normal vector is a unit vector (magnitude 1)

20. Vertex Normals • Many APIs just use normals at vertices • Multiple Normal Approaches: • Set of Normals of adjacent polygons

21. Vertex Normals Continued • Single Vertex Normal Approaches: • Averages of all adjacent polygon normals • Set by user • Surface Curvature Normal

22. Calculating the Normal • For a curved surface: • Perpendicular to the Tangent of a surface • For a flat surface: • Perpendicular to the surface plane

23. Calculating a Normal for a Flat Polygon • Assume a triangle: • Vectors: • Normal:

24. Vertex Normals • Many APIs just use normals at vertices • Multiple Normal Approaches: • Set of Normals of adjacent polygons

25. Vertex Normals Continued • Single Vertex Normal Approaches: • Averages of all adjacent polygon normals • Set by user • Surface Curvature Normal

26. Vertex Normals • Vertex Normal • Calculated from adjacent polygon normals • Typically averaged: • Vertices shared between polygons will have the same vertex normal, and hence the same intensity.

27. Use of Vertex Normals: Shading • Curved surfaces are rendered as faceted approximations. • OpenGL supports smooth shading of faceted objects. • Smoother shading uses normal vectors. • At a point on the ideal surface, the normal vector points straight out.

28. Vertex Normals • An OpenGL vertex can have a vertex normal vector. • It should match the ideal surface’s normal vector at that location. • OpenGL smoothes the shading at the vertex, as if it were shading the ideal surface. • Calling sets the current vertex normal: glNormal3f(nx, ny, nz) • It applies to subsequent vertices until it is changed. • (nx, ny, nz) should have unit length. • transformations may change normals length

29. GL_POINTS GL_LINES GL_LINE_STRIP GL_LINE_LOOP GL_TRIANGLES GL_TRIANGLE_STIP GL_TRIANGLE_FAN GL_QUADS GL_QUAD_STRIP GL_POLYGON GL_LINES GL_POLYGON GL_LINE_STRIP GL_LINE_LOOP GL_POINTS GL_TRIANGLES GL_QUADS GL_TRIANGLE_STRIP GL_QUAD_STRIP OpenGL Model Representation