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Figure 5.2 The surface of the model is automatically voxelized right after sketching. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Figure 5.3 The user-drawn 3D curve is associated with the deformation grid. Since a curve consists of several vertices, the system searches for the nearest grid vertex from each curve vertex. The red points on the right figure represent handle vertices. . . . . . . . . . . . 39 Figure 5.4 An example of distance approximation. The distance from the handle vertex is calculated according to the distance from the neighbour vertex dn. . . . . . . . . . . . . . . . . . . . . . . . . 40 Figure 5.5 Once the curve has been drawn, the handle vertices are found. Each vertex stores the approximate shortest distance to the handle, found using Dijkstra’s algorithm. . . . . . . . . . . . . . . . 40 Figure 5.6 The vertex V stores two shortest distances. dA and dB are the shortest distances from the curve A and the curve B, respectively. 41 Figure 5.7 When the handle vertex (hv) is translated with T1, the vertices in the red circle are influenced. The same thing happens with T2. 42 Figure 5.8 Deformation for point based surface representations can be achieved with (a), however inverse deformation is required to deform an implicit surface (b). vi is a vertex of the deformation grid. . . . 43 Figure 5.9 q is influenced by vertices vi. The amount of the influence is calculated with the Wyvill function. The amount is used as the weight for the interpolation. . . . . . . . . . . . . . . . . . . . 43 Figure 5.10The field value of q1 is calculated with the Wyvill function. Nev- ertheless, the field value of q2 cannot be calculated because no vertex influences q2. In this case, the system simply returns 0 as the field value of q2. . . . . . . . . . . . . . . . . . . . . . . . . 44 x
Figure 5.11An example deformation procedure with the duck shown in Fig- ure 5.2. The first column shows the results of the visualized implicit model. The second column shows the scalar field im- ages which were sampled from a slice along a plane. The original shape of the duck is shown in (a). By pushing the bill of the duck, the duck is squashed interactively in interactive deformation (b), however the scalar field outside of the deformation field is lost. Once the model has been deformed, the scalar field of the duck is re-calculated with variational warping (c). A good scalar field can be preserved with variational warping and the field is cached for further modeling. The deformed voxels are also shown in (d). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Figure 5.12Variational construction result. (a) shows the deformation dur- ing interactive deformation approximation and (b) is the result after applying variational construction. As can be seen, the crest and feather of the model are lost due to the grid resolution. The details of the model can not be preserved. The upper scalar field is also not constructed well because of the same reason. . . . . 47 Figure 5.13Variational warping result. (b) is the result after applying variational warping. Although the same grid resolution as Figure 5.12 is used, the details of the model is preserved. Also, a better scalar field is constructed compared to the scalar field in Figure 5.12. . 49 Figure 5.14Evaluation of the interactive deformation approximation pass. The point primitive (a) is deformed by pulling the upper right of it. The discontinuity of the scalar field is generated near the iso- surface (b). A crease is also created in the discontinuity region when a blending operator is applied to the scalar field (c). . . . 51 Figure 5.15Evaluation of variational warping. Variational warping is applied to the scalar field of the deformed point primitive shown in Figure 5.14b (a). Unlike Figure 5.14c, a smooth transition can be created when a blending operator is applied (b). A CSG operator also creates sharp edges with keeping continuity (c). . 51 xi
Page 1 and 2: Free-Form Deformation for Implicit
Page 3 and 4: Supervisory Committee Dr. Brian Wyv
Page 5 and 6: 3.1.1 Lattice-Based FFD . . . . . .
Page 7 and 8: List of Figures Figure 1.1 Deformat
Page 9: Figure 4.2 The rigidity of the surf
Page 13 and 14: ACKNOWLEDGEMENTS First I would like
Page 15 and 16: of lattice manipulation is that man
Page 17 and 18: Figure 1.1: Deformation for implici
Page 19 and 20: Chapter 2 Introduction to Implicit
Page 21 and 22: Figure 2.1: Skeletons and skeletal
Page 23 and 24: Figure 2.3: Variational interpolati
Page 25 and 26: fields fA(p) and fB(p) can be simpl
Page 27 and 28: Figure 2.6: Voxelization. A set of
Page 29 and 30: model, even novice users can create
Page 31 and 32: Chapter 3 Background and Previous W
Page 33 and 34: Figure 3.1: Lattice-based FFD. The
Page 35 and 36: Figure 3.2: An implicit model befor
Page 37 and 38: into several systems. Chameleon [22
Page 39 and 40: as follows: • ShapeShop enables t
Page 41 and 42: Chapter 4 Deformation Interface Thi
Page 43 and 44: 4.2 Interface Design This deformati
Page 45 and 46: Figure 4.4: Grid and curve visualiz
Page 47 and 48: global deformation according to the
Page 49 and 50: Chapter 5 Deformation Algorithm Thi
Page 51 and 52: 5.2 Voxelization The user draws a c
Page 53 and 54: Figure 5.4: An example of distance
Page 55 and 56: Figure 5.7: When the handle vertex
Page 57 and 58: y the field value and then summed.
Page 59 and 60: 5.4 Scalar Field Re-construction Wh
Page 61 and 62:
5.4.2 Variational Warping Variation
Page 63 and 64:
outside the deformation field is ev
Page 65 and 66:
Chapter 6 Results and Conclusion Th
Page 67 and 68:
Figure 6.1: The dragon was deformed
Page 69 and 70:
Figure 6.3: The horse model was tra
Page 71 and 72:
6.2 Limitations There are a few lim
Page 73 and 74:
twisted scalar field cannot be re-c
Page 75 and 76:
Bibliography [1] Adzhiev, V., Cartw
Page 77 and 78:
[19] Gascuel, M.-P. An implicit for
Page 79 and 80:
[40] Pasko, A., Adzhiev, V., Sourin
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[60] Wyvill, B., Guy, A., and Galin
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