Lecture21-Curves-I

Lecture21-Curves-I - Curve 2 Curve Continuity C2 continuity...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
CS 455 – Computer Graphics Curves
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Parametric Function Complexity We need functions that give us enough flexibility to represent interesting surfaces We want to keep the complexity reasonable We will work primarily with 3rd order (cubic) polynomials § lower degree does not give us enough flexibility § higher degree or more complex functions require too much computation § can get curves such as:
Background image of page 2
Curve Formulation
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Curve Continuity Often times we want to join multiple curves together The continuity is measured by how smoothly they join C0 continuity refers to curves that join at their endpoints Curve 1 Curve 2
Background image of page 4
Curve Continuity Typically we will want curves that join with more smoothness than just C0 continuity C1 continuity refers to curves that join at their endpoints, and also have first derivatives equal at the join point Curve 1
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Curve 2 Curve Continuity C2 continuity gives us common joint points, and 1st and 2nd derivatives equal at the joint point. Two curves that join at the endpoint and have the nth derivatives equal at that point are called Cn continuous. For most applications, we want to join curves with either C1 or C2 continuity. Why Cubic Curves? Get upto C2 continuity. Need more non-0 derrivatives to get more continuity. Minimal curviness when fitting a set of points. Specifying position and derivative at beginning and end is nice. Numerical computation issues are well-behaved enough Artist Friendly Controls We want the same expressive power we see in powerpoint curves You specify endpoints and tangents, math does the rest Curves Curves Now for quadratic curves. Cubics...
View Full Document

Page1 / 12

Lecture21-Curves-I - Curve 2 Curve Continuity C2 continuity...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online