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Joshi_Rutvik_HW4.nb
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CSE 577
Instructor : Dianne Hansford
Homework 4 : B-spline curve design
Due : April 22, 2016 by midnight\
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Part 1.
Design a 3D nonplanar pretzel using a closed, cubic B-spline. The pretzel \
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Extra credit: create an interesting rendering/colormap/texture map.
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"\n\nPart 2.\nLet ",
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"(t) describe a 3D, nonplanar cubic curve. How many points of zero curvature \
can this curve have at most? Explain.\n\n"
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Ans :-
The equation for the curvature is
k(t) = || x\[CloseCurlyQuote](t) ^ x\[CloseCurlyQuote]\[CloseCurlyQuote](t) \
|| / || x\[CloseCurlyQuote](t) ||^3
if the numerator of the equation || x\[CloseCurlyQuote](t) ^ x\
\[CloseCurlyQuote]\[CloseCurlyQuote](t) || = 0 then the curvature of that \
point is zero k(t) = 0.
The cubic non planar curve has two inflation points for that the curve \
changes its direction (negative to positive or positive to negative) by \
solving the equation
x\[CloseCurlyQuote](t) ^ x\[CloseCurlyQuote]\[CloseCurlyQuote](t) = 0
So, 3D nonplanar cubic curbe has at most 2 points of zero curvature.
\
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