Week 2 - Modelling surfaces Flashcards
Types of surface
Triangle Mesh
Subdivisional surfaces
Bicubic bezier
Tensor product spline/surface patch
Implicit surface
explicit surface
parametric surface
point set surface
What is the most common type of surface?
Triangle mesh
What surface is ultimately drawn by the GPU?
Triangle Mesh, the 3d analogue of polylines
What do subdivision surfaces do with a coarse polygonal mesh
Creates a smooth curved surface from them
Tensor product splines are the surface analog of
spline curves
Explicit formulas
Have the exact formula to represent the surface
Procedural surfaces
Surfaces of revolution, generalised cylinder, swept surfaces
In what domain are surfaces of revolution popular?
medial images
Tensor product spline/surface patch pros/cons
Pros:
- Smooth
- Defined by reasonably small number of points
Cons:
Harder to render, usually converted to triangles at render time anyway
Tricky to ensure continuity at patch boundaries, some extensions to solve this problem:
- Rational spline, splines in homogeneous coordinates
- NURB surfaces - Non-uniform rational bsplines
–Nurbs (nerves?) we have a ratio of polynomials and non-uniform locations for the control points
Chaikin’s algorithm
corner cutting
essentially an extension of bspline curves , explained by castoral construction from week 1
sculpturing
With whatever fancy geometry we have, we can always start with a cube and keep sculpturing around it using corner cutting subdivision.
As long as the goal has the same topology as the starting object
Pros / cons of implicit surface representation
Pros:
- Very efficient, can easily check if a point is on the surface, or inside or outside because we know the formula
- Also efficient for boolean operations which we need in graphics
- Can handle weird topology for animations
- Always easy to do sketchy modelling, where we don’t care much about the final product
Cons:
- Not be allowed to easily generate a point on the surface, because every time we add another control point, we need to generate a new formula
What surface representation is used in modern modelling?
Implicit surfaces, using point sets to define them. Some cool math involved in this, including MLS moving
Point set surface
A noisy 3d point cloud, with no connectivity. We can derive a reasonable surface from them.
Can be derived from scanners, laser range scans give us the points directly.
modelling is simple, we can add points to it without messing up the whole surface
