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Geometric Modeling

Geometric Modeling. Geometric Modeling. Volumetric Collection device obtains regular grid of measurement values Examples: CT, MRI, PET, Ultrasound Values are interpreted/visualized with color, transparency, texture Example: Marching Cubes. Geometric Modeling. Procedural

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Geometric Modeling

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  1. Geometric Modeling

  2. Geometric Modeling • Volumetric • Collection device obtains regular grid of measurement values • Examples: CT, MRI, PET, Ultrasound • Values are interpreted/visualized with color, transparency, texture • Example: Marching Cubes

  3. Geometric Modeling • Procedural • Geometry is calculated by some equation or algorithm and rendered. The algorithms can be as creative as one can imagine, but we can divide them into two types: fractal (natural) and non-fractal (man-made) • Examples:

  4. Geometric Modeling • Implicit Surface • Geometry is assumed at all points that satisfy equation f(x, y, z) = 0 • Examples: A sphere centered at (a, b, c) of radius r is the set of all points satisfying the equation (x-a)2 + (y-b)2 + (z-c)2 = r2 • Multiple implicit surfaces can be grouped together to create more complicated shapes.

  5. Geometric Modeling • Parametric Patch • Geometry is calculated using parametric equations and varying a parametric parameter over some range. • Examples: • Video describing parametric equations (see 1:17-5:20) • The equation p(u, v) = [ u v k1u2+k2v2 ] describes the parabola seen here as u and v vary over [0, 1]

  6. Geometric Modeling • Modeling with Higher-Order Surfaces (Quadrics and Cubics) • Quadrics: Supports common shapes such as circles, ellipses, and parabolas • Examples: • Cubics: General purpose patches allows for favorable continuity conditions • Examples:

  7. Geometric Modeling • Other Modeling Methods • Constructive Solid Geometry builds intricate shapes from simple ones using set operations. • Example: • Terrain Generators are a procedural modeling tool, but often customized for generating “terrain-like” models (i.e., usually controlled by some type of height map)

  8. Geometric Modeling • Modeling with Planer Polygons • This is by far the most common case in (non-engineering) computer graphics today • Engineering models prefer bi-cubic patches for analysis and then convert these patches into polygonal meshes for display • Commodity display hardware is optimized for planer polygons • Further optimized for triangles (and sometime quads). Why? • Types of Polygonal Models • Extrusions • Replications • Symmetric • Bi-symmetry • Surface of Revolution • Compositions of Simpler Surfaces

  9. 3D Modeling Terminology • Coordinate System: • XYZ (RGB) • Right Handed • Handedness effects rotation • Pos rotation follows finger curl • Reference Frames • Model • World • Eye • View Model World View Eye

  10. 3D Modeling Terminology • Normal • Front Face • Back Face • Transformations • Translate • Rotate • Scale • Shear • Mirror

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