Shape Modeling with Point-Sampled Geometry Mark Pauly, Richard Keiser, Leif P. Kobbelt, Markus Gross (ETH Zurich and RWTH Aachen)

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Shape Modeling withPoint-Sampled GeometryMark
Pauly, Richard Keiser, Leif P. Kobbelt, Markus
Gross(ETH Zurich and RWTH Aachen)
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Abstract

• Modeling framework with point-sampled geometry
• Hybrid representation
• Point clouds
• Implicit surface with MLS
• General operations on models
• Booleans operations
• Deformations

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Surface representations
Introduction

• Implicit surfaces level sets, RBF
• Topology defined
• Non-intuitive to control
• Rendering is slow
• Parametric surfaces splines, subdivision
  surfaces, triangle meshes
• Simplicity
• Extreme deformation
• Connectivity information

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Hybrid surface

• Unstructured points
• Implicit surface
• Signed distance
• Normal defined
• Boolean operations
• Preserve shard edges

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Freeform modeling

• Global deformation
• Preserve the sampling density
• Tools
• Push, pull, twist and etc.
• Topology control

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A component in a modeling system

• Takes scanner inputs
• Rendering techniques
• QSplat Zwicker 01
• Rusinkiwicz 00
• Botsch 02
• Fast with free LOD

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Related work

• Points primitive
• Szeliski and Tonnesen 92
• Oriented particles
• Physical simulation
• Witkin and Heckbert 94
• Blend operation
• Limited deformations
• Freeform modeling
• Chang and Rackwood 94
• Wires system

• Dynamically sampling
• Welch and Witkin 94
• Trangle mesh
• Vertex split and edge collapse
• Kobbelt 00
• Multiresolution
• Dynamic mesh connectivity

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Hybrid surface model

• Input points with attributes
• Moving least squares (MLS)

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Moving least squares
4. proj(r)qg(0,0)n

1. Local reference domain
2. Minimize to find H
3. Minimize to find g

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MLS kernel function

• Small h cause Gaussian decay faster
• Small h means approximation more local
• MLS act as an low pass filter

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Adaptive MLS

• If the sampling of points is adaptive
• k ranges 620

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Boolean operations

• CSG in a binary tree.
• Computing the boolean operation
• Find
• New set of intersection curves
• Crisp curves

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Inside outside classification
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Optimization

• 90 can be approximated
• Else use MLS projection to find y
• Local coherence
• If x is within the sphere center at x, radius is

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Classification table

• Points in Q1 is picked from P1 only if
• p is outside of surface defined by P2
• Similarly for Q2

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Intersection curves

• A set of points for intersection curves
• Find points near the intersection using the
  distance function
• Closest point pairs (q1 in Q1, q2 in Q2)
• r in the intersection of the tangent planes
• Project r to new q1 and q2
• Repeat step 3 to 5 for 3 iterations

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Intersection curves diagram
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Adaptive refinement

• Match sample density
• Use a simple subdivision
• New p for the Newton iteration

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Rendering sharp creases

• Surface splatting Zwicker 01
• Surfel elliptical splat
• Intersection curve points
• Clip against two normals

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Sharp creases results
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Freeform deformation

• Bending, twisting, stretching, compressing
• Interactive speed
• Intuitive control
• Global operation

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Deformable regions

• Region zero not selected
• Region one handle

d00, d1x, tb(0/(0x))0
d0dist(p and x0)x, d10, tb(x/(x0))1
d0dist(p and x0)x, d1min(p and x1)y,
tb(x/(xy))
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Applying translation and rotation

• Demo

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Blending function
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Rotation and twisting results
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Topology control

• Self intersections
• Collision detection
• Nearest point for each point in Xd
• Within the sphere collision free

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Collision handling

• Undo (disallow self intersections)
• Union (sharp edges)
• Blending
• Inter particle potential Szeliski 92
• Define a local neighborhood

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Topology results
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Dynamic sampling

• Cause Distortion and insufficient sampling
• Goal insert and remove points
• Feature Interpolate attributes
• Color
• Texture value

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Measuring surface stretch

• u and v are on the tangent plane
• Orthogonal
• Unit length
• Local anisotropy
• Ratio of the two eigenvalues
• Split a point into two

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Dynamic sampling results
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Filter operations

• Problem what to do with the new points
• Relaxation Turk 92
• Confined radius of influence
• Projection back to the tangent plane

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Interpolation (with Zombies)

• Scalar values
• Drifting happens when split happens
• Zombies are fixed
• Only used for the attributes
• Delete after each edit operation

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Interpolation results
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Downsampling

• Special case
• Shrink then grow
• Lost values cause blur
• Preserve old value
• Garbage collection

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Results and discussion

• Pointshop3D
• Multiresolution surface modeling
• Detail vectors Zorin 97
• Spectral decomposition Guskov 99

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(No Transcript)
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69,706 295,220
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69,268 222,955
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25,020 non-uniform
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100,269
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Implementation

• Closest points query
• Kd-tree
• Building 300,000 points in 0.23 s
• Querying 10 points in 4.5e-6 and 6.2e-6 s

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Dynamic updates

• Boolean classification
• Two static structure
• Free-form deformation
• No update until an edit session is done
• Collision detection
• Only for deformable region with the zero region
• Cannot handle collision of deformable regions
• Dynamically sampling
• Linsen 02
• Dynamic update at insertions and relaxation

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Performance

• No connectivity to update
• Handling one million points
• Pointshop3D software rendering
• 50 of the total computation is rendering
• Software renderer Botsch 02
• Hardware renders Rusinkiewicz 00

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Conclusion and future work

• A solid framework for modeling
• Provides basic operations
• Extends to traditional surface modeling
  techniques
• Efficiency and performance
• Future work
• Hairy or furry models, plants
• Dynamic simulation