## Displaced subdivision surfaces (2000)

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Venue: | Siggraph 2000, Computer Graphics Proceedings, Annual Conference Series, pages 85–94. ACM Press / ACM SIGGRAPH |

Citations: | 139 - 1 self |

### BibTeX

@INPROCEEDINGS{Lee00displacedsubdivision,

author = {Aaron Lee and Henry Moreton},

title = {Displaced subdivision surfaces},

booktitle = {Siggraph 2000, Computer Graphics Proceedings, Annual Conference Series, pages 85–94. ACM Press / ACM SIGGRAPH},

year = {2000},

publisher = {Addison Wesley Longman}

}

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### Abstract

In this paper we introduce a new surface representation, the displaced subdivision surface. It represents a detailed surface model as a scalar-valued displacement over a smooth domain surface. Our representation defines both the domain surface and the displacement function using a unified subdivision framework, allowing for simple and efficient evaluation of analytic surface properties. We present a simple, automatic scheme for converting detailed geometric models into such a representation. The challenge in this conversion process is to find a simple subdivision surface that still faithfully expresses the detailed model as its offset. We demonstrate that displaced subdivision surfaces offer a number of benefits, including geometry compression, editing, animation, scalability, and adaptive rendering. In particular, the encoding of fine detail as a scalar function makes the representation extremely compact. Additional Keywords: geometry compression, multiresolution geometry, displacement maps, bump maps, multiresolution editing, animation.

### Citations

1178 | Progressive meshes
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Citation Context ... line segments visible in Figure 5f correspond to rays with positive displacements.) 4.1 Simplification to control mesh We simplify the original mesh using a sequence of edge collapse transformations =-=[22]-=- prioritized according to the quadric error metric of Garland and Heckbert [16]. In order to produce a good domain surface, we restrict some of the candidate edge collapses. The main objective is that... |

1004 | Surface simplification using quadric error metrics
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Citation Context ...nts.) 4.1 Simplification to control mesh We simplify the original mesh using a sequence of edge collapse transformations [22] prioritized according to the quadric error metric of Garland and Heckbert =-=[16]-=-. In order to produce a good domain surface, we restrict some of the candidate edge collapses. The main objective is that the resulting domain surface should be able to express the original mesh using... |

707 | Obb-tree: A hierarchical structure for rapid interference detection
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Citation Context ...istance from the limit point to the original surface along the normal (Figure 5f). The directed line formed by the point and normal is intersected with the original surface, using a spatial hierarchy =-=[17]-=- for efficiency. We disregard any intersection point if the intersected surface is oriented in the wrong direction with respect to the directed line. If multiple intersection points remain, we pick th... |

648 |
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Citation Context ...e locally along its normal (see Figure 1). In this paper we use the Loop [27] subdivision surface scheme, although the representation is equally well defined using other schemes such as Catmull-Clark =-=[5]-=-. Both subdivision surfaces and displacement maps have been in use for about 20 years. One of our contributions is to unify these two ideas by defining the displacement function using the same subdivi... |

554 | A signal processing approach to fair surface design
- TAUBIN
- 1995
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Citation Context ...acement pyramid, we compute the samples at any level l<k by filtering the limit displacements of level l+1. We considered several filtering operations and opted for the non-shrinking filter of Taubin =-=[35]-=-. Because the displacement magnitudes are kept small, their filtering is not extremely sensitive. In many rendering situations much of the visual detail is provided by bump mapping. As has been discus... |

551 |
Differential Geometry of Curves and Surfaces
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Citation Context ... used as a modeling primitive, then the displacements may be quite large and the full expression must be � � evaluated. The difficult term nˆ u = nu / nu may be derived using the Weingarten equations =-=[12]-=-. Equivalently, it may be expressed as: � � nu − nˆ ( nu ⋅ nˆ ) � � � � � nˆ u = � where nu = Puu × Pv + Pu × Puv . n At a regular (valence 6) vertex, the necessary partial derivatives are given by a ... |

541 |
Smooth subdivision surfaces based on triangles
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Citation Context ...e displaced subdivision surface, consists of a control mesh and a scalar field that displaces the associated subdivision surface locally along its normal (see Figure 1). In this paper we use the Loop =-=[27]-=- subdivision surface scheme, although the representation is equally well defined using other schemes such as Catmull-Clark [5]. Both subdivision surfaces and displacement maps have been in use for abo... |

540 | Stuetzle: Multiresolution analysis of arbitrary meshes
- Eck, DeRose, et al.
- 1995
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Citation Context ...editing. To make this multiresolution framework practical, several techniques have been developed for constructing a parameterization of an arbitrary surface over a triangular base domain. Eck et al. =-=[14]-=- use Voronoi/Delaunay diagrams and harmonic maps, while Lee et al. [26] track successive mappings during mesh simplification. In contrast, displaced subdivision surfaces do not support an arbitrary pa... |

349 | Multiresolution analysis for surfaces of arbitrary topological type
- Lounsbery, DeRose, et al.
- 1997
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Citation Context ...ping and displacement mapping. They advocate combining them into a unified representation and resorting to true displacement mapping only when necessary. Multiresolution subdivision: Lounsbery et al. =-=[28]-=- apply multiresolution analysis to arbitrary surfaces. Given a parameterization of the surface over a triangular domain, they compress this (vector-valued) parameterization using a wavelet basis, wher... |

333 | Geometry compression - DEERING - 1995 |

314 |
Efficient bit allocation for an arbitrary set of quantizers
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Citation Context ... each subband, we use the embedded quantizer and embedded entropy coder described in Taubman and Zakhor [37]. The subbands are merged using the bit allocation algorithm described by Shoham and Gersho =-=[34]-=-, which is based on integer programming. An alternative would be to use the compression scheme of Kolarov and Lynch [24], which is a generalization of the wavelet compression method in [33]. Figure 10... |

304 |
Simulation of wrinkled surfaces
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- 1978
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Citation Context ... artifacts. Kobbelt et al. [23] use a similar framework to express the geometry of one mesh as a displacement from another mesh, for the purpose of multiresolution shape deformation. Bump maps: Blinn =-=[3]-=- introduces the idea of perturbing the surface normal using a bump map. Peercy et al. [31] present recent work on efficient hardware implementation of bump maps. Cohen et al. [8] drastically simplify ... |

303 |
Multirate 3-D Subband Coding of Video
- Taubman, Zakhor
- 1994
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Citation Context ...al values. For each level, we treat the difference coefficients over allfaces as a subband. For each subband, we use the embedded quantizer and embedded entropy coder described in Taubman and Zakhor =-=[37]-=-. The subbands are merged using the bit allocation algorithm described by Shoham and Gersho [34], which is based on integer programming. An alternative would be to use the compression scheme of Kolaro... |

277 | Piecewise smooth surface reconstruction
- Hoppe, DeRose, et al.
- 1994
(Show Context)
Citation Context ...chemes defining smooth surfaces have been introduced by Catmull and Clark [5], Doo and Sabin [13], and Loop [27]. More recently, these schemes have been extended to allow surfaces with sharp features =-=[21]-=- and fractionally sharp features [11]. In this paper we use the Loop subdivision scheme because it is designed for triangle meshes. DeRose et al. [11] define scalar fields over subdivision surfaces us... |

256 | Geometric compression through topological surgery
- Taubin, Rossignac
- 1996
(Show Context)
Citation Context ...ing [16]. The simplified meshes are obtained using the scheme of Garland and Heckbert [16]. For mesh compression, we use the VRML compressed binary format inspired by the work of Taubin and Rossignac =-=[36]-=-. We vary the quantization level for the vertex coordinates to obtain different compressed meshes, and then adjust our displacement map compression parameters to obtain a displaced surface with matchi... |

240 | MAPS: multiresolution adaptive parameterization of surfaces
- Lee, Sweldens, et al.
- 1998
(Show Context)
Citation Context ...niques have been developed for constructing a parameterization of an arbitrary surface over a triangular base domain. Eck et al. [14] use Voronoi/Delaunay diagrams and harmonic maps, while Lee et al. =-=[26]-=- track successive mappings during mesh simplification. In contrast, displaced subdivision surfaces do not support an arbitrary parameterization of the surface, since the parameterization is given by t... |

239 | Spherical wavelets: Efficiently representing functions on the sphere
- Schröder, Sweldens
- 1995
(Show Context)
Citation Context ...bdivision surface. A simple example of a displaced surface is terrain data expressed as a height field over a plane. The case of functions over the sphere has been considered by Schröder and Sweldens =-=[33]-=-. Another example is the 3D scan of a human head expressed as a radial function over a cylinder. However, even for this simple case of a head, artifacts are usually detectable at the ear lobes, where ... |

221 | Fitting smooth surfaces to dense polygon meshes
- Krishnamurthy, Levoy
- 1996
(Show Context)
Citation Context ...generalizing this concept to arbitrary surfaces is that of finding a smooth underlying domain surface that can express the original surface as a scalar-valued offset function. Krishnamurthy and Levoy =-=[25]-=- show that a detailed model can be represented as a displacement map over a network of B-spline patches. However, they resort to a vector-valued displacement map because the detailed model is not alwa... |

202 |
Subdivision surfaces in character animation
- DeRose, Kass, et al.
- 1998
(Show Context)
Citation Context ...been introduced by Catmull and Clark [5], Doo and Sabin [13], and Loop [27]. More recently, these schemes have been extended to allow surfaces with sharp features [21] and fractionally sharp features =-=[11]-=-. In this paper we use the Loop subdivision scheme because it is designed for triangle meshes. DeRose et al. [11] define scalar fields over subdivision surfaces using subdivision masks. Our scalar dis... |

188 | Interactive multiresolution mesh editing
- Zorin, Schröder, et al.
- 1997
(Show Context)
Citation Context ...ace over a triangular domain, they compress this (vector-valued) parameterization using a wavelet basis, where the basis functions are defined using subdivision of the triangular domain. Zorin et al. =-=[39]-=- use a similar subdivision framework for multiresolution mesh editing. To make this multiresolution framework practical, several techniques have been developed for constructing a parameterization of a... |

184 | W.: Real time compression of triangle mesh connectivity
- GUMHOLD, STRASSER
- 1998
(Show Context)
Citation Context ...has recently been an active area of research. Several clever schemes have been developed to concisely encode the combinatorial structure of the mesh connectivity, in as few as 1-2 bits per face (e.g. =-=[18]-=- [35]). As a result, the major portion of a compressed mesh goes to storing the mesh geometry. Vertex positions are typically compressed using quantization, local prediction, and variable-length delta... |

125 | Normal meshes
- Guskov, Vidimce, et al.
- 2000
(Show Context)
Citation Context ...wflake” surface, where the domain surface cannot be made much simpler than the original surface. Fortunately, fine detail in most practical surfaces is expressible as an offset surface. Guskov et al. =-=[20]-=- represent a surface by successively applying a hierarchy of displacements to a mesh as it is subdivided. Their construction allows most of the vertices to be encoded using scalar displacements, but a... |

118 |
Bidirectional reflection functions from surface bump maps
- Cabral, Max, et al.
- 1987
(Show Context)
Citation Context ...ercy et al. [31] present recent work on efficient hardware implementation of bump maps. Cohen et al. [8] drastically simplify meshes by capturing detail in the related normal maps. Both Cabral et al. =-=[4]-=- and Apodaca and Gritz [1] discuss the close relationship of bump mapping and displacement mapping. They advocate combining them into a unified representation and resorting to true displacement mappin... |

86 |
Advanced RenderMan: Creating CGI for motion pictures
- Apodaca, Gritz
- 1999
(Show Context)
Citation Context ...t map. Displacement maps: The idea of displacing a surface by a function was introduced by Cook [9]. Displacement maps have become popular commercially as procedural displacement shaders in RenderMan =-=[1]-=-. The simplest displacement shaders interpolate values within an image, perhaps using standard bicubic filters. Though displacements may be in an arbitrary direction, they are almost always along the ... |

83 | Multiresolution shape deformations for meshes with dynamic vertex connectivity
- Kobbelt, Bareuther, et al.
- 2000
(Show Context)
Citation Context ...their domain surface is not smooth since it is a polyhedron. As shown in Section 5.3, animating a displaced surface using a polyhedral domain surface results in many surface artifacts. Kobbelt et al. =-=[23]-=- use a similar framework to express the geometry of one mesh as a displacement from another mesh, for the purpose of multiresolution shape deformation. Bump maps: Blinn [3] introduces the idea of pert... |

81 | Interactive multiresolution surface viewing - Certain, Popović, et al. - 1996 |

74 |
Behavior of recursive division surfaces near extraordinary points, Computer-Aided Design
- Doo, Sabin
- 1978
(Show Context)
Citation Context ...ation and hierarchical backface culling (Section 5.5). 2. PREVIOUS WORK Subdivision surfaces: Subdivision schemes defining smooth surfaces have been introduced by Catmull and Clark [5], Doo and Sabin =-=[13]-=-, and Loop [27]. More recently, these schemes have been extended to allow surfaces with sharp features [21] and fractionally sharp features [11]. In this paper we use the Loop subdivision scheme becau... |

71 |
Smooth Transitions between Bump Rendering Algorithms
- Becker, Max
- 1993
(Show Context)
Citation Context ...displacement magnitudes are kept small, their filtering is not extremely sensitive. In many rendering situations much of the visual detail is provided by bump mapping. As has been discussed elsewhere =-=[2]-=-, careful filtering of bump maps is both important and difficult. 4.6 Conversion results The following table shows execution times for the various steps of the conversion process. These times are obta... |

52 | Efficient bump mapping hardware
- Peercy, Airey, et al.
- 1997
(Show Context)
Citation Context ...sh as a displacement from another mesh, for the purpose of multiresolution shape deformation. Bump maps: Blinn [3] introduces the idea of perturbing the surface normal using a bump map. Peercy et al. =-=[31]-=- present recent work on efficient hardware implementation of bump maps. Cohen et al. [8] drastically simplify meshes by capturing detail in the related normal maps. Both Cabral et al. [4] and Apodaca ... |

48 | Surface fitting with hierarchical splines - Forsey, Bartels - 1995 |

48 | Modeling and rendering for realistic facial animation
- Marschner, Guenter, et al.
- 2000
(Show Context)
Citation Context ...de the control mesh, and manipulated the skeleton to deform this mesh. (The complete animation is on the accompanying video.) Another application of our representation is the fitting of 3D head scans =-=[30]-=-. For this application, it is desirable to re-use a common control mesh structure so that deformations can be conveniently transferred from one face model to another. 5.4 Scalability Depending on the ... |

24 | Multiresolution rendering with displacement mapping
- Gumhold, H¨uttner
- 1999
(Show Context)
Citation Context ...es on the mesh. The recent work on surface pasting by Chan et al. [7] and Mann and Yeung [29] uses the similar idea of adding a vector-valued displacement map to a spline surface. Gumhold and Hüttner =-=[19]-=- describe a hardware architecture for rendering scalar-valued displacement maps over planar triangles. To avoid cracks between adjacent triangles of a mesh, they interpolate the vertex normals across ... |

23 | Fast backface culling using normal masks
- Zhang, KE
- 1997
(Show Context)
Citation Context ...ering performance, we avoid rendering regions of the displaced subdivision surface that are entirely facing away from the viewpoint. We achieve this using the normal masks technique of Zhang and Hoff =-=[38]-=-. . On the finely subdivided version of the domain surface, we compute the vertex normals of the displaced surface as described in Section 3. We convert these into a normal mask for each subdivided fa... |

22 |
Appearance preserving simplification
- Cohen, Olano, et al.
- 1998
(Show Context)
Citation Context ...ion. Bump maps: Blinn [3] introduces the idea of perturbing the surface normal using a bump map. Peercy et al. [31] present recent work on efficient hardware implementation of bump maps. Cohen et al. =-=[8]-=- drastically simplify meshes by capturing detail in the related normal maps. Both Cabral et al. [4] and Apodaca and Gritz [1] discuss the close relationship of bump mapping and displacement mapping. T... |

15 |
Local smooth surface interpolation: a classification. Computer Aided Geometric Design 7
- Peters
- 1990
(Show Context)
Citation Context ...from a continuous analytic surface representation. However, it is difficult to piece together multiple displacement maps while maintaining smoothness. One encounters the same vertex enclosure problem =-=[32]-=- as in the stitching of B-spline surfaces. While there are well-documented solutions to this problem, they require constructions with many more coefficients (9× in the best case), and may involve solv... |

14 |
trees. Computer Graphics
- Cook
(Show Context)
Citation Context ...their method does not consider whether the approximation residual is expressible as a scalar displacement map. Displacement maps: The idea of displacing a surface by a function was introduced by Cook =-=[9]-=-. Displacement maps have become popular commercially as procedural displacement shaders in RenderMan [1]. The simplest displacement shaders interpolate values within an image, perhaps using standard b... |

10 | Compression of functions defined on surfaces of 3D objects
- Kolarov, Lynch
- 1997
(Show Context)
Citation Context ...ds are merged using the bit allocation algorithm described by Shoham and Gersho [34], which is based on integer programming. An alternative would be to use the compression scheme of Kolarov and Lynch =-=[24]-=-, which is a generalization of the wavelet compression method in [33]. Figure 10 and Table 1 show results of our compression experiments. We compare storage costs for simplified triangle meshes and di... |

6 | Cylindrical surface pasting
- Mann, Yeung
- 1999
(Show Context)
Citation Context ...r-valued displacement map. In their scheme, the patch network is constructed manually by drawing patch boundaries on the mesh. The recent work on surface pasting by Chan et al. [7] and Mann and Yeung =-=[29]-=- uses the similar idea of adding a vector-valued displacement map to a spline surface. Gumhold and Hüttner [19] describe a hardware architecture for rendering scalar-valued displacement maps over plan... |

1 |
World space surface pasting. Graphics Interface '97
- Chan, Mann, et al.
(Show Context)
Citation Context ...k together with a vector-valued displacement map. In their scheme, the patch network is constructed manually by drawing patch boundaries on the mesh. The recent work on surface pasting by Chan et al. =-=[7]-=- and Mann and Yeung [29] uses the similar idea of adding a vector-valued displacement map to a spline surface. Gumhold and Hüttner [19] describe a hardware architecture for rendering scalar-valued dis... |