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RayTracing%20Point%20Set%20Surfaces

# RayTracing%20Point%20Set%20Surfaces - r = r a point close...

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Ray Tracing Point Set Surfaces Authors: Anders Adamson, Mark Alexa Also see: Point Set Surfaces Marc Alexa, Johannes Behr, Daniel Cohen-Or, Shachar Fleishman, David Levin, Claudio T. Silva

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Goal
H is found by minimizing Point on the surface r is computed by projection Note: Local feature lengths are larger than h .

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Computing the plane Nonlinear optimization: Unknowns are {n, t}
Computing the plane Nonlinear optimization: Start with t=0 Compute n. Refine initial value using Powell Iteration.

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Ray-Surface Intersection Converge iteratively by projecting points from the ray to the sruface

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Unformatted text preview: r = r , a point close to the surface. • Intersect the local polynomial defined by r . Let the intersection point be r 1 . • If ( r-r 1 ) < ε stop else Set r = r 1 . Repeat the previous step. Data Structure • Define a Sphere around each point with radius h . • Create a spatial hierarchy of spheres. Example Rendering with shadow Results of the ray tracing procedure applied to raw point data. The afarensis (early human) model consists of 150,000 points acquired with a structured light scanner from a physical model. Example Rendering (with refraction and shadow)...
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