Progressive meshes

Hugues Hoppe

article1996SIGGRAPH3,441 citations

Introduces a continuous-resolution triangle mesh representation based on invertible edge collapse transformations that enables progressive transmission, smooth level-of-detail geomorphing, and view-dependent selective refinement while preserving surface appearance attributes.

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Highly detailed triangle meshes have become essential for realism in computer graphics yet create heavy demands on rendering, storage, and transmission. The paper therefore introduces the progressive mesh representation, which stores any triangle mesh as a coarse base mesh plus a sequence of vertex-split records that incrementally restore the original. This structure directly targets five practical needs: automatic simplification, smooth level-of-detail transitions, progressive transmission, compact encoding, and view-dependent refinement.

The work evaluates both the representation itself and a new simplification algorithm that constructs it. The algorithm repeatedly collapses edges while minimizing an energy function that accounts for geometric error, spring regularization, scalar attributes such as color and normals, and the geometry of discontinuity curves. It records the inverse vertex-split operations to produce the progressive mesh directly. Experiments were performed on several scanned and modeled meshes ranging from a few thousand to roughly 150,000 faces, with quantitative timing and bit-rate results reported for each.

The progressive mesh format yields three to five most important outcomes. First, any intermediate mesh complexity can be retrieved in linear time simply by applying a prefix of the split sequence. Second, smooth visual transitions (geomorphs) can be constructed between any two such meshes without perceptible popping. Third, the same records enable progressive transmission that recovers the exact original mesh losslessly once all data arrive. Fourth, the encoding size remains competitive with specialized single-resolution compressors while also supporting selective refinement inside a view frustum or near silhouettes. Fifth, the appearance-preserving simplification produces meshes whose faces adapt naturally to material boundaries and scalar fields, often retaining visual fidelity at far lower face counts than geometry-only methods.

These capabilities matter because they let applications trade accuracy for speed on demand, stream geometry over modest bandwidth links, and reduce storage without separate preprocessing pipelines. The representation therefore lowers both computational cost and transmission latency while preserving the visual quality that motivates the use of detailed models in the first place.

The paper recommends deploying progressive meshes for web-based 3-D delivery, continuous level-of-detail rendering, and multigrid finite-element meshes. It also lists concrete next steps: an explicit optimization metric for normals, support for articulated models, and addition of spatial indexing to accelerate selective refinement. Before large-scale adoption, further validation on production pipelines and measurement of end-to-end bandwidth savings would be prudent.

The reported results rest on a modest number of representative models and a prototype implementation that was not tuned for maximum compression; quantitative error bounds are not provided, and the method assumes manifold triangle meshes. Within those boundaries the evidence for the listed functional benefits is consistent and reproducible.

Microsoft bandwidth geometric modeling lossless Progressive Mesh Mesh Simplification Level of Detail

hhoppe/Mesh-processing-library Hoppe (1996).pdf

Paper: Surface reconstruction from unorganized points, Hugues Hoppe et al. (1992). Understanding surface reconstruction from unorganized point sets provides foundational insights into handling arbitrary topology before reading about progressive mesh generation.

Paper: Surface simplification using quadric error metrics, Michael Garland et al. (1997). This paper builds directly upon the progressive mesh framework by introducing quadric error metrics to optimize vertex contraction and surface simplification.

Abstract

Highly detailed geometric models are rapidly becoming common-place in computer graphics. These models, often represented as complex triangle meshes, challenge rendering performance, transmission bandwidth, and storage capacities. This paper introduces the progressive mesh (PM) representation, a new scheme for storing and transmitting arbitrary triangle meshes. This efficient, lossless, continuous-resolution representation addresses several practical problems in graphics: smooth geomorphing of level-of-detail approximations, progressive transmission, mesh compression, and selective refinement.

In addition, we present a new mesh simplification procedure for constructing a PM representation from an arbitrary mesh. The goal of this optimization procedure is to preserve not just the geometry of the original mesh, but more importantly its overall appearance as defined by its discrete and scalar appearance attributes such as material identifiers, color values, normals, and texture coordinates. We demonstrate construction of the PM representation and its applications using several practical models.

Topics

bandwidth geometric modeling lossless optimization triangle mesh object appearance

Keywords

Progressive Mesh Mesh Simplification Level of Detail Geomorph Progressive Transmission Mesh Compression Selective Refinement Edge Collapse Vertex Split Energy Function

1 INTRODUCTION
2 MESHES IN COMPUTER GRAPHICS
3 PROGRESSIVE MESH REPRESENTATION
3.1 Overview
3.2 Geomorphs
3.3 Progressive transmission
3.4 Mesh compression
3.5 Selective refinement
4 PROGRESSIVE MESH CONSTRUCTION
4.1 Background: mesh optimization
4.2 Overview of the simplification algorithm
4.3 Preserving surface geometry ( $E_{dist} + E_{spring}$ )
4.4 Preserving scalar attributes ( $E_{scalar}$ )
4.5 Preserving discontinuity curves ( $E_{disc}$ )
4.6 Permitting changes to topology of discontinuity curves
5 RESULTS
6 RELATED WORK
Advantages of PM over MRA:
7 SUMMARY AND FUTURE WORK

Knowls

Knowl 1 — Progressive Mesh Representation
definition
A triangle mesh $M$ is defined as a tuple $M = (K, V, D, S)$ , where:
- $K$ is a simplicial complex specifying the connectivity (adjacency of vertices, edges, and faces);
- $V = \{v_1, \dots, v_m\}$ is the set of vertex positions defining the geometry in $\mathbb{R}^3$ ;
- $D = \{d_f : f \in K\}$ is the set of discrete attributes (such as shader material identifiers) associated with faces $f = \{j, k, l\} \in K$ ;
- $S = \{s_{(v, f)} : (v, f) \in \text{corners}(K)\}$ is the set of scalar attributes (such as diffuse color $(r, g, b)$ , normals $(n_x, n_y, n_z)$ , and texture coordinates $(u, v)$ ) associated with mesh corners $(v, f)$ , where a corner is a vertex-face pair.
An edge collapse transformation $\text{ecol}(\{v_s, v_t\})$ unifies two adjacent vertices $v_s$ and $v_t$ into a single vertex $v_s$ , removing vertex $v_t$ and the two adjacent faces $\{v_s, v_t, v_l\}$ and $\{v_t, v_s, v_r\}$ .

The inverse of an edge collapse is a vertex split transformation $\text{vsplit}(s, l, r, t, A)$ , which introduces a new vertex $v_t$ near $v_s$ , adds two new faces $\{v_s, v_t, v_l\}$ and $\{v_t, v_s, v_r\}$ (or one face if on a boundary where $v_r = 0$ ), and updates local attribute information $A$ (the positions of $v_s$ and $v_t$ , discrete face attributes, and scalar corner attributes).

An arbitrary triangle mesh $\hat{M} = M^n$ is simplified into a coarse base mesh $M^0$ through a sequence of $n$ successive edge collapses:

$M^n \xrightarrow{\text{ecol}_{n-1}} M^{n-1} \xrightarrow{\text{ecol}_{n-2}} \dots \xrightarrow{\text{ecol}_0} M^0$

The progressive mesh (PM) representation of $\hat{M}$ is defined as the tuple:

$(M^0, \{\text{vsplit}_0, \text{vsplit}_1, \dots, \text{vsplit}_{n-1}\})$

Applying any prefix of $i$ vertex splits to $M^0$ yields an intermediate approximating mesh $M^i$ , providing a continuous-resolution representation that reconstructs $\hat{M} = M^n$ losslessly.
Knowl 2 — Progressive Mesh Construction via Priority Queue Edge Collapses
algorithm
The progressive mesh construction algorithm simplifies an arbitrary mesh $\hat{M} = M^n$ into a base mesh $M^0$ using only edge collapse transformations, generating the sequence of inverse vertex split records $\text{vsplit}_i$ . Candidate edge collapses are prioritized using an energy metric $\Delta E = E_{K'} - E_K$ that evaluates geometric error, attribute deviation, and discontinuity curve preservation.
Input: Initial mesh $\hat{M} = (K, V, D, S)$ , point sample set $X \subset \hat{M}$ , sharp edge point sample set $X_{\text{disc}}$ , attribute weights $c_{\text{scalar}}$ , stopping threshold $m_{\text{target}}$
Output: Base mesh $M^0$ and sequence of detail records $\{\text{vsplit}_0, \dots, \text{vsplit}_{n-1}\}$
$M \leftarrow \hat{M}$
$Q \leftarrow$ empty priority queue
for each candidate edge collapse $\text{ecol}(\{v_s, v_t\})$ in $M$ do
    if $\text{ecol}(\{v_s, v_t\})$ is legal (manifold-preserving) then
         $\Delta E \leftarrow \text{ComputeCollapseCost}(M, \{v_s, v_t\}, X, X_{\text{disc}}, c_{\text{scalar}})$
        Insert $\{v_s, v_t\}$ into $Q$ keyed by $\Delta E$
    end if
end for
$n \leftarrow 0$
$\text{records} \leftarrow$ empty list
while $Q$ is not empty and $\text{FaceCount}(M) > m_{\text{target}}$ do
     $\{v_s, v_t\} \leftarrow \text{ExtractMin}(Q)$
    if $\text{ecol}(\{v_s, v_t\})$ remains legal then
        Record corresponding $\text{vsplit}_n(s, l, r, t, A)$ into $\text{records}$
        Apply $\text{ecol}(\{v_s, v_t\})$ to $M$
         $n \leftarrow n + 1$
        for each edge $\{v_j, v_k\}$ in neighborhood of the collapsed edge do
            if $\text{ecol}(\{v_j, v_k\})$ is legal then
                 $\Delta E \leftarrow \text{ComputeCollapseCost}(M, \{v_j, v_k\}, X, X_{\text{disc}}, c_{\text{scalar}})$
                Update or insert $\{v_j, v_k\}$ in $Q$ with priority $\Delta E$
            else
                Remove $\{v_j, v_k\}$ from $Q$ if present
            end if
        end for
    end if
end while
$M^0 \leftarrow M$
Reverse the order of $\text{records}$ so that $\text{vsplit}_i$ inverts $\text{ecol}_i$
Renumber vertices and faces in $M^0$ and $\text{records}$ sequentially
return $M^0, \text{records}$
Knowl 3 — Geomorph Construction Between Arbitrary PM Resolution Levels
model/method
Given a coarse mesh $M^c$ and a finer mesh $M^f$ ( $0 \le c < f \le n$ ) from a progressive mesh sequence, a geomorph $M^G(\alpha)$ with blend parameter $\alpha \in [0, 1]$ defines a continuous visual transition such that $M^G(0)$ has the shape and appearance of $M^c$ and $M^G(1) = M^f$ .

The mesh connectivity of $M^G(\alpha)$ is fixed to that of $M^f$ , denoted $K^f$ . A surjective ancestor map $A^c : \{1, \dots, m_0 + f\} \to \{1, \dots, m_0 + c\}$ maps each vertex index $j$ of $M^f$ to its corresponding ancestor vertex in $M^c$ :

$A^c(j) = \begin{cases} j, & j \le m_0 + c \\ A^c(s_{j - m_0 - 1}), & j > m_0 + c \end{cases}$

where $s_i$ is the split vertex index from $\text{vsplit}_i$ .

The vertex positions $v_j^G(\alpha)$ of $M^G(\alpha)$ linearly interpolate between the ancestor position in $M^c$ and the final position in $M^f$ :

$v_j^G(\alpha) = \alpha v_j^f + (1 - \alpha) v_{A^c(j)}^c$

Discrete face attributes require no interpolation: faces in $M^f$ that are absent in $M^c$ have their vertices mapped to identical ancestors at $\alpha = 0$ , rendering those triangles degenerate (zero area) and invisible at the coarse level.

Scalar corner attributes $s_{(v, f)}$ are interpolated across $\alpha$ . If a corner $(v, f)$ in $M^f$ is newly created and not present in $M^c$ , its coarse attribute value is obtained by backtracking through ancestor corners in intermediate meshes that share the identical attribute value; if no ancestor corner shares the value, the attribute remains constant over $\alpha$ .
Knowl 4 — Selective Refinement Using Closest Living Ancestors
model/method
Selective refinement adapts mesh detail locally by evaluating an application-defined boolean predicate $\text{REFINE}(v)$ (such as view-frustum inclusion, screen projected face area, or silhouette edge proximity) on candidate vertex splits.

When selectively refining an initial mesh $M^c$ by iterating through $\text{vsplit}_c, \dots, \text{vsplit}_{n-1}$ , applying a split $\text{vsplit}_i(s_i, l_i, r_i, A_i)$ directly requires vertices $v_{l_i}$ and $v_{r_i}$ to exist. Because adjacent vertices outside the refinement region may not have been created, the split condition is relaxed using a dynamically updated closest living ancestor map $A': \{1, \dots, m_0 + n\} \to \{1, \dots, m_0 + n\}$ :

$A'(j) = \begin{cases} j, & \text{if } v_j \text{ exists in the current mesh} \\ A'(s_{j - m_0 - 1}), & \text{otherwise} \end{cases}$

The split transformation is applied if and only if:
1. $v_{s_i}$ is present in the current mesh (i.e., $A'(s_i) = s_i$ ) and the vertices $v_{A'(l_i)}$ and $v_{A'(r_i)}$ are both currently adjacent to $v_{s_i}$ ; and
2. $\text{REFINE}(v_{s_i})$ evaluates to true.
When executed, the transformation is parameterized as $\text{vsplit}(s_i, A'(l_i), A'(r_i), A_i)$ . This prevents cracking and avoids stalling refinement when expected neighbors lie outside the active region.
Knowl 5 — Geometric Energy Optimization and Adaptive Spring Regularization
equation
The geometric error of approximating a dense set of sampled points $X \subset \mathbb{R}^3$ by a mesh $M = (K, V)$ is evaluated and minimized using the energy terms:

$E_{\text{geom}}(V) = E_{\text{dist}}(V) + E_{\text{spring}}(V)$

where the distance energy measures the sum of squared Euclidean distances from the sampled points to the surface:

$E_{\text{dist}}(V) = \sum_{x_i \in X} d^2(x_i, \phi_V(|K|)) = \sum_{x_i \in X} \min_{b_i \in |K|} \|x_i - \phi_V(b_i)\|^2$

and the spring regularization energy places zero-rest-length springs along edges to prevent under-constrained optimization:

$E_{\text{spring}}(V) = \sum_{\{j, k\} \in K} \kappa \|v_j - v_k\|^2$

The spring constant $\kappa$ is computed adaptively for each candidate edge collapse based on the ratio $r = \frac{|X_{\text{local}}|}{F_{\text{local}}}$ of point samples to faces in the local transformation neighborhood:

$\kappa = \begin{cases} 10^{-2}, & r < 4 \\ 10^{-4}, & 4 \le r < 8 \\ 10^{-8}, & r \ge 8 \end{cases}$

When evaluating $\text{ecol}(\{v_s, v_t\})$ , the unified vertex position $v_s$ is optimized by alternating between calculating projection parameterizations $b_i$ and solving a linear least-squares system for $v_s$ , testing three starting positions $v_s = (1 - \alpha)v_s^{i+1} + \alpha v_t^{i+1}$ for $\alpha \in \{0, 0.5, 1\}$ and selecting the candidate that achieves minimal energy.
Knowl 6 — Scalar Attribute Optimization at Mesh Corners
model/method
To preserve continuous and piecewise continuous scalar fields (such as color, normals, or texture coordinates) during mesh simplification without computing high-dimensional non-geometric spatial projections, scalar attribute error is measured using fixed geometric parameterizations $b_i \in |K|$ :

$E_{\text{scalar}}(V, S) = (c_{\text{scalar}})^2 \sum_{x_i \in X} \|\underline{x}_i - \underline{\phi}_V(b_i)\|^2$

where $\underline{x}_i \in \mathbb{R}^d$ is the sampled scalar attribute at point $x_i$ , $\underline{\phi}_V(b_i)$ is the interpolated scalar field at barycentric coordinate $b_i$ , and $c_{\text{scalar}}$ is a user-defined scaling weight relating scalar attribute error to geometric error.

For corner attributes at a unified vertex $v_s$ :
1. The set of corners incident to $v_s$ is partitioned into disjoint equivalence classes based on matching attribute values across adjacent faces.
2. For each independent partition, the optimal scalar attribute value is solved via an uncoupled linear least-squares problem using the parameterizations $b_i$ obtained during geometric optimization.
3. Attributes with bounded ranges (e.g., color components $(r, g, b) \in [0, 1]$ ) are clipped to their valid intervals.
4. Unit surface normals $(n_x, n_y, n_z)$ are not solved via non-linear least squares; instead, the new normal at $v_s$ is linearly interpolated from the normals of $v_s^{i+1}$ and $v_t^{i+1}$ using the parameter $\alpha \in \{0, 0.5, 1\}$ that minimized the geometric energy.
Knowl 7 — Preservation and Topological Penalization of Discontinuity Curves
model/method
Discontinuity curves arise from surface boundaries, discrete face attribute differences ( $d_{f_l} \ne d_{f_r}$ ), and scalar corner attribute differences ( $s_{(v_j, f_l)} \ne s_{(v_j, f_r)}$ or $s_{(v_k, f_l)} \ne s_{(v_k, f_r)}$ ) across an edge $\{v_j, v_k\}$ , designated as $\text{sharp}(v_j, v_k)$ .

A candidate edge collapse $\text{ecol}(\{v_s, v_t\})$ modifies the topology of discontinuity curves if any of the following conditions hold (where $\#\text{sharp}(v)$ is the number of sharp edges incident to $v$ ):
- $\text{sharp}(v_s, v_l) \land \text{sharp}(v_t, v_l)$
- $\text{sharp}(v_s, v_r) \land \text{sharp}(v_t, v_r)$
- $\#\text{sharp}(v_s) \ge 1 \land \#\text{sharp}(v_t) \ge 1 \land \neg\text{sharp}(v_s, v_t)$
- $\#\text{sharp}(v_s) \ge 3 \land \#\text{sharp}(v_t) \ge 3 \land \text{sharp}(v_s, v_t)$
- $\text{sharp}(v_s, v_t) \land \#\text{sharp}(v_s) = 1 \land \#\text{sharp}(v_t) \ne 2$
- $\text{sharp}(v_s, v_t) \land \#\text{sharp}(v_t) = 1 \land \#\text{sharp}(v_s) \ne 2$
Geometric accuracy along discontinuity curves is maintained by sampling points $X_{\text{disc}}$ from sharp edges in $\hat{M}$ and adding an energy term $E_{\text{disc}}(V)$ measuring squared distances from $X_{\text{disc}}$ to the sharp edges of $M$ .

To allow simplification of small or distant features without strictly locking topology, edge collapses that alter discontinuity curve topology are permitted but penalized by adding an energy penalty to $\Delta E$ :

$\Delta E_{\text{topo}} = |X_{\text{disc}, \{v_s, v_t\}}| \|v_s - v_t\|^2$

where $|X_{\text{disc}, \{v_s, v_t\}}|$ is the count of sharp-edge sample points projecting onto edge $\{v_s, v_t\}$ .
Knowl 8 — Progressive Mesh Encoding and Compression
model/method
The progressive mesh representation allows compact encoding of both mesh connectivity and geometry:
- Connectivity Encoding: For each vertex split $\text{vsplit}_i(s_i, l_i, r_i, A_i)$ , vertex $v_{s_i}$ is identified using $\lceil \log_2 n \rceil$ bits. The neighbor vertices $v_{l_i}$ and $v_{r_i}$ are chosen from the ordered neighborhood of $v_{s_i}$ (average degree 6). Storing the permutation index requires $\lceil \log_2 P_2^6 \rceil = \lceil \log_2 30 \rceil = 5$ bits, resulting in approximately $(\lceil \log_2 n \rceil + 5)n$ bits for overall connectivity.
- Geometry Encoding: Coordinates are quantized to 16-bit fixed precision integers. For an edge collapse with starting position $v_n \in \{v_s, v_t, \frac{v_s + v_t}{2}\}$ , the split positions $v_s^{i+1}$ and $v_t^{i+1}$ are delta-encoded as either $\{v_s - v_n, v_t - v_n\}$ or $\{\frac{v_s+v_t}{2} - v_n, \frac{v_t - v_s}{2}\}$ . The quantized deltas are compressed using separate Huffman tables for each candidate type, achieving geometry storage of 31 to 50 bits per vertex.
- Attribute Encoding: Material identifiers and corner scalar attributes are delta-predicted from adjacent faces in $M^i$ using control bits.

Knowl 9 — Quantitative Performance of PM Construction and Compression

data/table

Quantitative performance and parameter configurations for constructing progressive meshes from five test models on a 150 MHz SGI Indigo2 workstation (128 MB memory) are shown below. The table details original mesh complexity ( $m_0 + n$ vertices, face count), base mesh complexity ( $m_0$ vertices, face count), point sampling parameters, discontinuity curve sample count $|X_{\text{disc}}|$ , geometry compression rate in bits per vertex, and total optimization runtime.

Object	Original $\hat{M}$		Base $M^0$		User param.		$\|X_{\text{disc}}\|$	$V$ bits/ $n$	Time (min)
	$m_0+n$	#faces	$m_0$	#faces	$\|X\| - (m_0+n)$	$c_{\text{color}}$
cessna	6,795	13,546	97	150	100,000	-	46,811	46	23
terrain	33,847	66,960	3	1	0	-	3,796	46	16
mandrill	40,000	79,202	3	1	0	0.1	4,776	31	19
radiosity	78,923	150,983	1,192	1,191	200,000	0.01	74,316	37	106
fandisk	6,475	12,946	27	50	10,000	-	5,924	50	19

The results show that complex models with up to 150,983 faces can be reduced to minimal base meshes ( $1$ to $1,191$ faces) while retaining the full sequence of detail records for exact reconstruction. Quantized, Huffman-coded geometry storage ranges from 31 to 50 bits per vertex across all datasets.

Knowl 10 — Properties and Trade-offs of Progressive Meshes Compared to Multiresolution Wavelet Analysis
theoretical result
Progressive meshes (PM) and surface multiresolution analysis (MRA) wavelets both provide continuous-resolution representations, but exhibit distinct structural properties:
1. Lossless vs. Approximate Recovery: MRA requires detail wavelet coefficients to lie on a domain with subdivision connectivity, recovering arbitrary meshes $\hat{M}$ only within an $\epsilon$ -tolerance. In contrast, PM is strictly lossless ( $M^n = \hat{M}$ ) and operates on arbitrary irregular connectivity.
2. Approximation Quality: Approximating meshes $M^i$ in a PM sequence can alter connectivity freely, optimizing triangle distributions to geometric features and outperforming subdivision-restricted MRA meshes at equivalent face counts.
3. Discontinuity Representation: PM can introduce surface creases and sharp boundaries at arbitrary locations and resolution levels. MRA cannot effectively capture creases unless they align parametrically with base mesh edges, and cannot naturally represent discrete face attributes without non-continuous Haar bases.
4. Parameterization and Error Bounds: MRA provides a smooth parameterization between resolutions that facilitates multiresolution editing, provides guaranteed maximum error bounds $\epsilon$ , and supports independent compression of geometry and color. PM yields piecewise linear, non-smooth parameterizations and lacks strict maximum error bounds in its standard construction.

Coverage note — No substantial contributed material was omitted; all primary contributions regarding progressive mesh representation, geomorphing, selective refinement, energy-based optimization, attribute preservation, compression, and experimental comparisons are covered.

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Citation

MLA

Hoppe, H. “Progressive Meshes”. Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, 1996, pp. 99–108, https://doi.org/10.1145/237170.237216.

APA

Hoppe, H. (1996). Progressive meshes. Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, 99–108. https://doi.org/10.1145/237170.237216

Chicago

Hoppe, H. 1996. “Progressive Meshes”. Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, 99–108. https://doi.org/10.1145/237170.237216.

Harvard

Hoppe, H. (1996) “Progressive meshes”, Proceedings of the 23rd annual conference on Computer graphics and interactive techniques. ACM, pp. 99–108. Available at: https://doi.org/10.1145/237170.237216.

Vancouver

1. Hoppe H (1996) Progressive meshes. In: Proceedings of the 23rd annual conference on Computer graphics and interactive techniques. ACM, pp 99–108

BibTeX

@inproceedings{Hoppe_1996, series={SIGGRAPH96}, title={Progressive meshes}, url={http://dx.doi.org/10.1145/237170.237216}, DOI={10.1145/237170.237216}, booktitle={Proceedings of the 23rd annual conference on Computer graphics and interactive techniques}, publisher={ACM}, author={Hoppe, Hugues}, year={1996}, month=Aug, pages={99–108}, collection={SIGGRAPH96} }

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Progressive meshes

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — Progressive Mesh Representation

Knowl 2 — Progressive Mesh Construction via Priority Queue Edge Collapses

Knowl 3 — Geomorph Construction Between Arbitrary PM Resolution Levels

Knowl 4 — Selective Refinement Using Closest Living Ancestors

Knowl 5 — Geometric Energy Optimization and Adaptive Spring Regularization

Knowl 6 — Scalar Attribute Optimization at Mesh Corners

Knowl 7 — Preservation and Topological Penalization of Discontinuity Curves