Curve Aesthetics: Practice Page

Measuring Curve Aesthetics

Can a computer determine how nice a curve looks?

Question 1: Recalling that , explain why the value of A is smaller for flatter curves.

Question 2: Suppose that k' is continuous on [a,b] and the vertices of the curve have parameter values s1 < s2 < ... < sn. Prove that

This is the sum of the changes of curvatures at the vertices. Using this, explain why this means the value of A will be larger for a curve with lots of sharp corners than a curve with fewer, less-sharp corners.

Question 3: What's wrong with using arc length in practice?

Question 4: What changes if we integrate with respect to a parameter other than arc length?

Head back to the concepts page to learn how computers choose curves.


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