G8: Geometric Modeling Flashcards
What is geometric modeling?
Computational description of geometry
Involves data structures and algorithms to represent and process geometry.
What are the two types of geometry representation?
Implicit and Explicit
Each type serves different computational needs and advantages.
Define implicit geometry representation.
Defines equation that points on the surface must satisfy
Examples include algebraic surfaces, constructive solid geometry, and level sets.
Define explicit geometry representation.
Defines coordinates of points on the surface
Examples include Bezier curves, point clouds, and polygon meshes.
What is constructive solid geometry (CSG)?
Combine simple geometries using Boolean operations
Operations include union, difference, and intersection.
What are the Boolean operations used in CSG?
- Union: merge two objects
- Difference: subtract one object from another
- Intersection: take parts that are common to two objects
What is a signed distance function (SDF)?
Defines distance from the surface of a geometric shape
Used in implicit representations, such as algebraic surfaces.
What is an example of an implicit equation for a unit sphere?
x^2 + y^2 + z^2 = 1
This defines a sphere in 3D space.
What are point clouds in explicit geometry?
Set of points explicitly defined on a surface
Can be generated using spherical coordinates.
What are polygon meshes?
Define surface as a list of polygon vertex coordinates and connections
Most commonly represented as triangle meshes.
What is the computational trade-off for implicit representations?
- Easy inside/outside test
- Efficient representation
- Infinite resolution for simple shapes
However, hard to model complex geometries.
What are the advantages of explicit representations?
- Easier to model arbitrarily complex geometries
- Easier to sample points on surface
But, the inside/outside test is harder and resolution is finite.
Fill in the blank: Geometric modeling is very ______, as there are many different kinds of geometries we could want to represent.
challenging
What are example applications of geometric modeling in 2D?
- Typography
- Technical drawing
What are example applications of geometric modeling in 3D?
- Computer-aided design (CAD)
- Computer-aided manufacturing (CAM)
