Memory-Efficient Sliding Window Progressive Meshes Pavlo Turchyn University of Jyvaskyla

Memory-Efficient Sliding Window Progressive Meshes

Pavlo Turchyn

University of Jyvaskyla

Previous work• Progressive mesh is a data structure used to encode a large

number of mesh approximations– prog. mesh is similar to undo/redo mechanism of a text editor

– undo/redo keeps record of modifications done on text

– prog. mesh keeps record of modifications done on mesh

– by performing a certain number of modifications, one obtains the mesh with required number of triangles

• Progressive meshes are problematic for GPUs– mesh modifications must be performed on CPU

– each mesh instance requires updating its mesh data

– then the updated data has to be transferred from CPU to GPU

• Sliding window progressive mesh (SWPM) is a solution for view-independent LOD

Previous work

• Progressive mesh contains information what to do– which edge to collapse, which vertex is split

• SWPM contains triangulations– these “precomputed” triangulations can be stored in static on-GPU memory

buffers

Vertex split

Half-edge collapse

Half-edge collapse

“Simplified patch”

• Simplified patch is a patch after applying simplification operator that removes the inner vertex

• … that includes all triangles incident to a given vertex– this vertex is called inner vertex

Definitions

“Patch”

• Patch is a set of triangles

SWPM simplification algorithm


• Step 1: find the set of inner vertices– it follows from the patch definition that the inner vertices belong

to an independent set


• Step 1: find the set of inner vertices

• Step 2: construct the patches– criterion: a patch should not contain topologically isolated

triangles– all patches (denoted P1,...,P10 in our example) are stored in a list

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10

P1

P2

P3

P4

P6

P5

P9

P8

P10

P7



• Step 2: construct the patches around inner vertices

• Step 3: simplify the patches to obtain “simplified patches”– all inner vertices are removed– the simplified patches (denoted Q1,..., Q10) are appended to the list of patches

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10

Q1

Q2

Q3

Q4

Q6

Q5

Q9

Q8

Q10

Q7

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10


• This memory buffer is the main SWPM data structure

• Required number of triangles is obtained by choosing the corresponding subsequence of elements (“window”)– window size is 10 elements in our example

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10

• SWPM buffer holds triangles as triples of indices

• Such an index buffer consumes 4-6 times more memory than the index buffer of the initial mesh– often SWPM index buffer is bigger than vertex buffer of the mesh

• – C is the amount of memory for storing a single triangle

– is the number of triangles in the buffer

• In order to minimize the buffer size, we have to minimize

• Minimal is bounded

– where |T0| denotes the number of triangles in the initial mesh

SWPM index dataset size

buffer_size_in_bytes C

0 02 | | 11| |T T

• Under certain assumptions, the following estimate holds

– is the average degree (valence) of the inner vertices

– is a mesh-dependent parameter that reflects triangulation structure

Feasible triangles quality

SWPM index dataset size

0| | ( 1)T d

3d 4d 5d 6d

d

d

Mesh connectivity optimization

16% dataset reduction

• Idea: change mesh connectivity in order to reduce d

• Using this mesh as the initial one, we construct another SWPM buffer B1

Clustered patches

• This is the simplest mesh we can render from the buffer B0

– But what if we need even simpler mesh?

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10B0 :

(1)1P (1)

2P (1)3P (1)

4P (1)5P (1)

1Q (1)2Q (1)

3Q (1)4Q (1)

5QB1 :

• Then, obtain simplified patches (by deleting all inner vertices)

• Idea: construct the “clustered patches”– a clustered patch is a patch (see definition)

– a clustered patch is a union of several consecutive simplified patches

Clustered patches

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10

h1P

Q1 Q2 Q3

h2P

Q4 Q5

h3P

Q6

h4P

Q7 Q8

h5P

Q9 Q10

Q1

Q2

Q3

Q4

Q6

Q5

Q9

Q8

Q10

Q7

Q4

Q6

Q5

Q9

Q8

Q10

Q7

Q6

Q9

Q8

Q10

Q7

Q9

Q8

Q10

Q7

Q9

Q10

B0 :

B1 :h1Q h

2Q h3Q h

4Q h5Q

• –

– thus, it is sufficient to store only the last part of B1

• Consider the buffers B0 and B1

– each clustered patch represents several consequtive simplified patches, so the first part of B1 is identical to the part of B0

Clustered patches


h1Q h

2Q h3Q h

4Q h5QB1 :

h1P h

2P h3P h

4P h5P

Clustering algorithm

• Input: the set of simplified patches

Q1

Q2

Q3

Q4

Q6

Q5

Q9

Q8

Q10

Q7



• Step 1: construct special vertices connectivity graph– any two vertices that belong to the same patch must be connected

with an edge

– resulting graph is not planar



• Step 1: construct special vertices connectivity graph

• Step 2: find the set of inner vertices– inner vertices belong to an independent set

– it is possible to use the same program code, which is used in the original SWPM simplification algorithm to find the set of inner vertices





• Step 3: construct the clustered patches– a clustered patch must include all simplified patches indcident to its

inner vertex

h1P

h2P

h3P h

4P

h5P





• Step 3: construct the clustered patches• Step 4: since clustered patch is a union of several consecutive simplified

patches, thus one may have to reorder the list of simplified patches

h1P

h2P

h3P h

4P

h5P

• Replace the last part of B0 with the last part of B1

– resulting buffer is also SWPM

The trade-off


h1Q h

2Q h3Q h

4Q h5QB1 :

• It is possible to trade the size of SWPM index dataset for the number of approximations stored in SWPM

h1Q h

2Q h3Q h

4Q h5QP1 P2 P3 P4 P5 P6 P7 P8 P9 P10

h1Q h

2Q h3Q h

4Q h5Q

Results• Reduction of SWPM index dataset:

– via connectivity optimization: ~20%

– via clustering: ~20%

– via optimization+clustering: ~30%

– via optimization+clustering+trade-off: >50%

• Clustering increases vertex cache miss ratio, but not significantly

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

LOD

ACMR

venus (no clustering)

venus (clustering)

venus (NVTriStrip)

Documents

Memory-Efficient Sliding Window Progressive Meshes Pavlo Turchyn University of Jyvaskyla