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Three_Dimensional_Object_Representation

# Three_Dimensional_Object_Representation - Chapter 10...

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Three-Dimensional Object Three-Dimensional Object Representation Representation Chapter 10

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Introduction Introduction Graphics scenes can contain many different kinds of objects No one method can describe all these objects Accurate models produce realistic displays of scenes Polygon and quadric surfaces Spline surfaces and construction techniques Procedural methods Physically-based modeling methods Octree encodings Boundary representations (B-reps) Space-partitioning representations
Polygon Surfaces Polygon Surfaces The most commonly used boundary represent- ation All surfaces are described with linear equations Simplify and speed up surface rendering and display of objects Precisely define a polyhedron For non-polyhedron objects, surfaces are tesselated Commonly used in design and solid modeling The wireframe outline can be display quickly

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Polygon Tables Polygon Tables Specify a polygon surface Geometric tables Vertex coordinates Spatial orientation of the polygon Attribute tables Degree of transparency Surface reflectivity Texture
Polygon Tables Polygon Tables Convenient organization for geometric data Vertex Table Edge Table Polygon Table v 1 v 2 v 3 v 4 v 5 E 1 E 2 E 3 E 4 E 5 E 6 S 1 S 2

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Polygon Tables Polygon Tables
Polygon Tables Polygon Tables Alternative arrangements Use just two tables: a vertex table and a polygon table Some edges could get drawn twice Use only a polygon table This duplicates coordinate information Extra information to the data tables Expand the edge table to include forward pointers into the polygon table Common edges between polygons Expand vertex table to contain cross-reference to corresponding edges

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Polygon Tables Polygon Tables Additional geometric information The slope for each edge Coordinate extents for each polygon Tests for consistency and completeness Every vertex is an endpoint for at least two edges Every edge is part of at least one polygon Every polygon is closed Each polygon has at least one shared edge Every edge referenced by a polygon pointer has a reciprocal pointer back to the polygon
Plane Equations Plane Equations The equation for a plane surface Ax + By + Cz +D = 0 By Cramer’s rule: Values of A,B,C and D are computed for each polygon and stored with the other polygon data

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Plane Equations Plane Equations Orientation of a plane surface Surface normal vector (A, B, C) Distinguish two sides of a surface “Inside” face “Outside” face The normal vector from inside to outside Viewing the outer side of the plane in a right- handed coordinate system Vertices are specified in counterclockwise direction
Plane Equations Plane Equations N=(A,B,C)

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Plane Equations Plane Equations
Plane Equations Plane Equations Identify a point (x, y, z) as either inside or outside a plane surface

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Three_Dimensional_Object_Representation - Chapter 10...

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