Defining Point-Set Surfaces Nina Amenta Yong Joo Kil SIGGRAPH 2004 - PowerPoint PPT Presentation

May 11, 2023 •502 likes •680 views

Defining Point-Set Surfaces Nina Amenta Yong Joo Kil SIGGRAPH 2004 11/2/2005 1 Point-Set Surfaces Surface S implied by the point cloud P No connectivity Surface properties Does x belong to S Project x to S 11/2/2005 2

Defining Point-Set Surfaces Nina Amenta Yong Joo Kil SIGGRAPH 2004 11/2/2005 1
Point-Set Surfaces • Surface S implied by the point cloud P – No connectivity • Surface properties – Does x belong to S – Project x to S 11/2/2005 2
MLS Surface • Given a point cloud P and a point r near P Weights depend on an 1. Find ( a, t ) that minimizes unknown plane r 11/2/2005 3
MLS Surface • Local minima over occur at discrete set of inputs ( a, t ) 2. Define f(r) to be x nearest to r 3. Stationary points of f form the MLS surface 11/2/2005 4
MLS Surface • Need to solve optimization problem to find f(r) – Expensive – Original paper proposed that one iteration is enough 11/2/2005 5
MLS Projection • Levin’s method, minimizes • Not a projection 11/2/2005 6
MLS Energy • Rewrite in terms of a point and a direction – Domain is 11/2/2005 7
Explicit MLS Definition • Define • MLS surface consists of points x such that 11/2/2005 8
9 Extremal Surfaces 11/2/2005
MLS Projection • PointShop method (linear approximation) – Alternate searching for x and best-fit plane 11/2/2005 10
New MLS Projection • Search for local minima along l x, n(x) – If this process converges, it produces a point on S 11/2/2005 11
12 Projection Results 11/2/2005
13 Comparison with Levin’s Method 11/2/2005
MLS for Surfels • Input (p i , a i ) 11/2/2005 14
Varying Normal Weight • Distance function favors the normal component All weights equal Only normals 11/2/2005 15
MLS for Weighted Point Clouds • Separate weight for each point 11/2/2005 16

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