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# Surface Simplification - PowerPoint PPT Presentation

Surface Simplification. Dr. Scott Schaefer. Surface Simplification. Given a closed polygon model, reduce the number of polygons and maintain appearance of the shape. 5804 tris. 2500 tris. 1000 tris. 500 tris. Reducing Polygons.

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Presentation Transcript

### Surface Simplification

Dr. Scott Schaefer

• Given a closed polygon model, reduce the number of polygons and maintain appearance of the shape

5804 tris

2500 tris

1000 tris

500 tris

• Perform local, topological operations to reduce number of polygons

• Vertex removal

• Perform local, topological operations to reduce number of polygons

• Vertex removal

• Edge Collapse

• Perform local, topological operations to reduce number of polygons

• Vertex removal

• Edge Collapse

• Face Collapse, …

• Perform local, topological operations to reduce number of polygons

• Vertex removal

• Edge Collapse

• Face Collapse, …

• How do we determine the order of edge collapse operations?

• Where do we place new vertex after collapse?

• Measures distance to infinite planes

• Measures distance to infinite planes

• Measures distance to infinite planes

symmetric 3x3

3x1

1x1

• Measures distance to infinite planes

symmetric 3x3

3x1

1x1

Requires 10 floats independent of number of polygons!!!

Add 10 numbers to combine QEFs!!!

• Place new vertex at minimum of error function

• Place new vertex at minimum of error function

• Place new vertex at minimum of error function

• Place new vertex at minimum of error function

Not invertible in flat areas or straight edges!!!

• Place new vertex at minimum of error function

Pseudoinverse minimizes |v|

• Let where c is a point we want to minimize the distance to

• Let where c is a point we want to minimize the distance to

• Let where c is a point we want to minimize the distance to

• Let where c is a point we want to minimize the distance to

• Compact representation (10 numbers)

• Fast to combine multiple functions (addition)

• Relatively easy to minimize (pseudoinverse)

• Suffers from numerical instabilities

• Build QEFs for each vertex

• For each edge

• Compute combined QEF and error

• Insert edge into priority queue sorted by error

• While poly # > target #

• Collapse edge

• Place new vertex at minimizer of QEF

• Place new vertex at minimizer of QEF

• QEF of new vertex is combined QEF

• Place new vertex at minimizer of QEF

• QEF of new vertex is combined QEF

• Remove all edges touching collapsed edge from priority queue

• Place new vertex at minimizer of QEF

• QEF of new vertex is combined QEF

• Remove all edges touching collapsed edge from priority queue

• Recompute QEF/error for all edges touching new vertex and insert into priority queue

• Edge collapse may alter topology of surface

• Test for topology change and exclude unsafe edge collapses

• Unsafe edge may become safe after another collapse

• Alternatively, perform two edge collapses

• Edge collapse may alter topology of surface

• Test for topology change and exclude unsafe edge collapses

• Unsafe edge may become safe after another collapse

• Alternatively, perform two edge collapses

unsafe edge collapses

• Edge collapse may alter topology of surface

• Test for topology change and exclude unsafe edge collapses

• Unsafe edge may become safe after another collapse

• Alternatively, perform two edge collapses

• Extremely fast

• Somewhat memory intensive

• Limits maximum surface size

• Greedy algorithm

• Does not guarantee optimal sequence of edge collapses!!!