Parametric Representations Flashcards
(30 cards)
Traditional function representations like y = f(x) are limited because…
They can only represent shapes wherein each x-coordinate corresponds to exactly one y-coordinate
Parametric representation expresses each axis as…
A function of one or more parameters
Traditional function representations struggle to represent curves because…
Many curves require multiple y-values for a single x
Polynomial parametric curves are extremely important in computer science, such as…
Linear, quadratic and cubic
Bezier curves are defined as…
A set of control points that influence the shape of the curve. The curve always passes through the first and last control points but generally not through intermediate ones.
In order to create a smooth join between two Bezier curves…
The end of one curve must be at the start of the second curve
To create a higher order continuity between two Bezier curves, the last two control points of the curve and the first two of the next must be…
Collinear
Subdivision is a technique that…
Allows us to create smooth curves
Chalkin’s algorithm starts with a polyline and…
Repeatedly generates new vertices at the first quarter and the last quarter of each line segment
C2 continuous subdivision uses complex rules to…
Create a cubic B-spline with higher order continuity
Doo-Sabin subdivision starts with a surface and…
Generates new vertices from weighted combinations of the original polygon vertices, using 9/16 for the primary vertex, 3/16 for adjacent vertices and 1/16 for the diagonal vertex
Catmull-Clark subdivision starts with a surface and…
Adds new face points (at face centers) and edge points (on edges), adjusting the original vertices based on surrounding geometry
Displacement maps are a tool that can be used for subdivision, allowing us to specify…
How far to move each point on the new smooth subdivision surface along its normal direction - similar to a height map, but after subdivision
Tessellation is a hardware technique built into most modern GPUs that uses a tesselation pipeline to…
Determine subdivision levels and new vertex positions dynamically based on camera distance or performance needs
Subdivision surfaces are used often in animation because… (pick one)
They maintain smoothness during deformation, animators can animate using a lower-quality model
Surface continuity is the…
Smoothness of the junction between two or more surfaces.
Catmull-Clark’s surface continuity is […], except for when […].
Is C2, except for when we have extraordinary points where vertices have anything other than 4 edges.
Extraordinary polygons are…
Faces that are not quadrilaterals
Bump mapping is different from displacement mapping because…
Bump mapping creates the illusion of detail via illumination tricks, while displacement mapping physically moves surface points to create actual detail
The pipeline for an animated scene is…
Create a low-quality model, animate it, then subdivide it, and use displacement mapping to adjust points for detail later
The Tessellation Control Shader manages…
How much tessellation to apply to each primitive, for both inner and outer tessellation levels
The Tessellation Evaluation Shader manages…
The actual position and attributes for each generated vertex after undergoing primitive generation
The tessellation pipeline consists of: Vertex Shader -> […] -> […] -> […] -> Geometry Shader -> Fragment Shader (HINT: parameter adjustments, application of tessellation, checking)
Tessellation Control -> Primitive -> Evaluation Shader
Tessellation levels control…
Subdivision intensity
