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Figure 2.6 Voxelization. A set of voxels are generated around the iso- surface. This figure was visualized by rasterizing the triangles viii extracted from the voxels. . . . . . . . . . . . . . . . . . . . . . 14 Figure 2.7 Polygonization with different voxel resolution. The polygonization quality increases from (a) to (c) as the voxel resolution does. 14 Figure 2.8 A BlobTree model. Spheres and a cylinder are stored at leaves as skeletal primitives. The face is composed of them using com- position operators at each interior node. In this BlobTree model, blend, union, difference, and bend nodes exist. . . . . . . . . . . 17 Figure 3.1 Lattice-based FFD. The embedded sphere is deformed according to the displacement of the control points which compose the lattice. 20 Figure 3.2 An implicit model before (a) and after (b) spatial deformation is applied. The green sphere represents a deformation field and the part inside the green sphere is bent. . . . . . . . . . . . . . 22 Figure 3.3 Sketch-based modeling procedure. The user draws a closed stroke on the screen as user input (a). The system then inflates the user stroke into a 3D shape along the vector normal to the screen (b). (c) is the inflated shape from a different angle. . . . . . . . . . 23 Figure 3.4 ShapeShop models. The piston model has sharp edges which were created with CSG operators (a). The complex branching structure of the heart model were constructed by blending several sketched simple components (b). Copyright Schmidt et al. Used with permission. . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Figure 3.5 ShapeShop user interface. When the user draws a stroke, the expectation list will be displayed on the screen. This list sug- gests available modeling operations with the drawn stroke. The parameter toolbar provides the sliders for the user to manipulate the parameters of the selected node. The user can control the position of the camera with the view toolbar. The BlobTree is automatically constructed according to the user input, but the user can manually edit the BlobTree of the model with the Blob- Tree editor if the user desires. . . . . . . . . . . . . . . . . . . 27 Figure 4.1 A peeling interface. Depending on how far the user pulls the curve, the deformation region is determined. . . . . . . . . . . . 29
Figure 4.2 The rigidity of the surface can also be manipulated by changing the growth rate. . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Figure 4.3 The user can pull the model from several positions with multiple curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Figure 4.4 Grid and curve visualization. (a) is the duck model deformed with multiple curves. The grid which defines the deformation of the duck can be visualized (b). Also, the user can make the curves invisible to see the final deformation result (c). . . . . . 32 Figure 4.5 Blending and CSG operators can be performed interactively after variational warping. This model is the one shown in Figure 4.3a to which Blending and CSG operators were applied. This model shows that Blending and CSG operators work after variational warping is applied because this model has smooth transitions and sharp edges. . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Figure 4.6 Stretched model (a). Original model (b). Squashed model (c). The user can stretch or squash the model just by pulling or push- ing the deformation curve the user drew. . . . . . . . . . . . . . 33 Figure 4.7 Deformation interface. When the user draws a curve on the surface, the deformation icon will be added to the expectation list. The user can manipulate the curve as a deformation handle by selecting the deformation icon. The rigidity slider and the icon for variational warping are provided in the parameter toolbar. 35 Figure 5.1 Framework of the deformation algorithm. The first row represents the user’s action and the second row represents the system’s action. The three steps of the deformation algorithm are shown in columns. The up-down arrow in the column of interactive deformation approximation represents the interaction between the user and the system. The system returns interactive feedback of approximated deformation appearance to the user according to the user input. Although the scalar field re-construction pass is a post-computing pass, the user can freely let the system go back to the interactive deformation approximation pass for iterative deformations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 ix
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: List of Figures Figure 1.1 Deformat
Page 11 and 12: Figure 5.11An example deformation p
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
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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
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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
Page 81:
[60] Wyvill, B., Guy, A., and Galin
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