Procedural Models

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Procedural Models - PowerPoint PPT Presentation

Procedural Models. How to easily generate complex data? Data from parameterized procedure and/or digitized Data amplification Ray trace directly v. convert to polygonal models and use z-buffer. Basic Procedural Approaches. composition from primitive shapes extrusion

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Procedural Models

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Presentation Transcript
Procedural Models
• How to easily generate complex data?
• Data from parameterized procedure and/or digitized
• Data amplification
• Ray trace directly v. convert to polygonal models and use z-buffer
Basic Procedural Approaches
• composition from primitive shapes
• extrusion
• surface of revolution
• lofting
• sweep operator
Composition

Procedurally generated

Controlled randomness

Sweep Operator

Combines extrusion, lofting, and surface of revolution

More sophisticated approaches
• CSG
• Subdivision surfaces
• Curves & surfaces
• Fractals
• Implicit functions
CSG:constructivesolid geometry
• primitive shapes
• union, difference, intersection
• tree structure representation
• Ray trace directly
• Evaluate to polyhedron with Boolean operators
• OpenGL rendering using stencil buffer
Subdivision surfaces

What is resulting limit surface?

• What is continuity of limit surface?
• Initial coursely defined geometry
• Refine geometry by
• rounding corners,
• subdividing faces and edges,
• smoothing faces
Subdivision surfaces
• Round corners
• Catmull-Clark
• Doo-Sabin
• Loop
• Butterfly
Curved surface patches
• Hermite curve & patches
• Bezier curve & patches
• Catmull-Rom spline
• B-spline
Hermite Curve
• Given: starting and ending points and tangents
• Determine cubic equation that satisfies constraints
Hermite Patch
• Given: starting and ending points and tangents
• Determine bicubic equation that satisfies constraints
Fractal geometry
• Objects that exhibit similarity under scale
• e.g., Koch curve
• Mathematically curious - continuous, infinite length, nowhere differentiable, bounded
Other fractal shapes

Mandelbrot set

Coastlines

Mountains

statistically self-similar under scale

Create mountains
• Subdivide triangle
• Displace upward
• Reduce amplitude of displacement
• Recurse on subdivisions
Implicit functions & isosurfaces
• f(x,y,z) = 0
• “density” function
• distance-based implicit functions
• Marching Cubes algorithm