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
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
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:
Forward Differencing Sample curve a many parameter values

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

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