3D Object Representations graphics scenes contain solid geometric objects trees, flowers, clouds, rocks, water representations surface ↔interior models.

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Presentation transcript:

3D Object Representations graphics scenes contain solid geometric objects trees, flowers, clouds, rocks, water representations surface ↔interior models procedural models physically based models boundary representations (B-reps) space-partitioning representations

Polygon Surfaces (1) set of surface polygons enclose object interior = Boundary Representation (“B- rep”) wireframe representation of a cylinder with back (hidden) lines removed

polygon tables (B-rep lists) geometric and attribute tables vertex, edge, polygon tables consistency, completeness checks

Polygon Surfaces: Data Structure

Polygon Surfaces: Plane Equation Ax+ By+ Cz+ D = 0 Cartesian coefficients A,B,C,D normal (A,B,C) distance to origin D

Polygon Meshes efficient data structures for tiled surfaces triangle strip n-2 triangles for n vertices

quadrilateral mesh (n-1)x(m-1) quadrilaterals

Curved Lines and Surfaces defined by mathematical functions (implicit, explicit, parametrically) set of data points (surface fitting) tesselation to get polygon mesh aproximation triangles quadrilaterals... (planar?!)

Quadric Surfaces defined by second degree equations (quadrics) – sphere – ellipsoid – torus – paraboloid – hyperboloid

Quadric Surfaces: Sphere implicit parametric φ φ θ π θ π φ θ π φ π sin cos sin, - cos cos, - /2 /2 z r y r x r = = ≤ ≤ x2 + y2 + z2 = r2