lecture04

lecture04 - CS 551/651 Advanced Graphics Arc Length...

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CS 551/651 Advanced Graphics Arc Length
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Assignment 1 Due Week from Thursday Building a Cubic Bézier curve OpenGL/Glut Insert up to 100 points Render Bézier curve using recursive subdivision Left mouse button to add, middle to move, and right to remove FLTK is extra credit
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Papers for Next Tuesday Presenters Needed Tour Into the Picture William T. Reeves, Particle systems - a technique for modelling a class of fuzzy objects. In SIGGRAPH '83, Computer graphics 17, 3, July 1983. " Animation of plant development ," Przemyslaw Prusinkiewicz, Mark S.Hammel, and Eric Mjolsness. Siggraph 1993.
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Arc Length Arc length is the distance along the curve To ensure constant speed of curve evaluation, perform arc length parameterization of curve Compute a mapping offline of arc length values to parameter values Analytically compute arc length
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Arc Length • Given parameters u 1 and u 2 , find LENGTH ( u 1 , u 2 ) Given an arc with length s and a parameter u 1 , find u 2 s.t. LENGTH (u 1 , u 2 ) is s Can we compute s = G(u) = distance from start of curve to point at u? If so, G -1 is used to build arc length parameterized curve: P(G -1 (s))
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Analytic Computation ( 29 = = = = 2 1 2 2 1 / ) 2 , 1 ( ) ( u u u u du du dP du du dP s u u length u P x ( 29 + + = + + = + + + = 2 1 2 2 2 2 3 2 3 2 3 / ) ( u u du c bu au s c bu au du dP d cu bu au u P Cubic curve example:
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Forward Differencing Sample curve a many parameter values
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lecture04 - CS 551/651 Advanced Graphics Arc Length...

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