1 / 10

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

kesler
Download Presentation

Geometric Modeling

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related