We present an algorithm for the automatic alignment of two 3D shapes (data and model), without any assumptions about their initial positions. The computes each surface point a descriptor based on local geometry that is robust to noise. A small number feature points are automatically picked from data shape according uniqueness value at point. For data, we use values model find potential corresponding points. then develop fast branch-and-bound distance matrix comparisons select optimal...

In architectural freeform design, the relation between shape and fabrication poses new challenges requires more sophistication from underlying geometry. The concept of conical meshes satisfies central requirements for this application: They are quadrilateral with planar faces, therefore particularly suitable design glass structures. Moreover, they possess a natural offsetting operation provide support structure orthogonal to mesh. Being discrete analogue network principal curvature lines,...

We introduce a computational framework for discovering regular or repeated geometric structures in 3D shapes. describe and classify possible present an effective algorithm detecting such patterns point- mesh-based models. Our method assumes no prior knowledge of the geometry spatial location individual elements that define pattern. Structure discovery is made by careful analysis pairwise similarity transformations reveals prominent lattice suitable model transformation space. optimization...

Computing a curve to approximate data points is problem encountered frequently in many applications computer graphics, vision, CAD/CAM, and image processing. We present novel efficient method, called squared distance minimization (SDM), for computing planar B-spline curve, closed or open, target shape defined by point cloud , that is, set of unorganized, possibly noisy points. show SDM significantly outperforms other optimization methods used currently common practice fitting. In SDM, starts...

We present a system for automatic reassembly of broken 3D solids. Given as input digital models the fragments, we analyze geometry fracture surfaces to find globally consistent reconstruction original object. Our pipeline consists graph-cuts based segmentation algorithm identifying potential surfaces, feature-based robust global registration pairwise matching and simultaneous constrained local multiple fragments. develop several new techniques in area processing, including novel integral...

We propose a framework for pairwise registration of shapes represented by point cloud data (PCD). assume that the points are sampled from surface and formulate problem aligning two PCDs as minimization squared distance between underlying surfaces. Local quadratic approximants function used to develop linear system whose solution gives best rigid transform given pair clouds. The is applied corresponding new orientation build. This process iterated until it converges. point-to-point...

We present a novel framework to treat shapes in the setting of Riemannian geometry. Shapes -- triangular meshes or more generally straight line graphs Euclidean space are treated as points shape space. introduce useful metrics this aid user design and modeling tasks, especially explore (approximately) isometric deformations given shape. Much work relies on an efficient algorithm compute geodesics spaces; end, we multi-resolution solve interpolation problem which amounts solving boundary...

We introduce a computational framework for discovering regular or repeated geometric structures in 3D shapes. describe and classify possible present an effective algorithm detecting such patterns point- meshbased models. Our method assumes no prior knowledge of the geometry spatial location individual elements that define pattern. Structure discovery is made by careful analysis pairwise similarity transformations reveals prominent lattice suitable model transformation space. optimization...

Fascinating and elegant shapes may be folded from a single planar sheet of material without stretching, tearing or cutting, if one incorporates curved folds into the design. We present an optimization-based computational framework for design digital reconstruction surfaces which can produced by folding. Our work not only contributes to applications in architecture industrial design, but it also provides new way study complex largely unexplored phenomena arising

We present a novel framework to treat shapes in the setting of Riemannian geometry. Shapes -- triangular meshes or more generally straight line graphs Euclidean space are treated as points shape space. introduce useful metrics this aid user design and modeling tasks, especially explore (approximately) isometric deformations given shape. Much work relies on an efficient algorithm compute geodesics spaces; end, we multi-resolution solve interpolation problem which amounts solving boundary...

The emergence of large-scale freeform shapes in architecture poses big challenges to the fabrication such structures. A key problem is approximation design surface by a union patches, so-called panels, that can be manufactured with selected technology at reasonable cost, while meeting intent and achieving desired aesthetic quality panel layout smoothness. production curved panels mostly based on molds. Since cost mold often dominates there strong incentive use same for multiple panels. We...

Self-supporting masonry is one of the most ancient and elegant techniques for building curved shapes. Because very geometric nature their failure, analyzing modeling such strutures more a geometry processing problem than classical continuum mechanics. This paper uses thrust network method analysis presents an iterative nonlinear optimization algorithm efficiently approximating freeform shapes by self-supporting ones. The rich networks leads us to close connections between diverse topics in...

We solve the form-finding problem for polyhedral meshes in a way which combines form, function and fabrication; taking care of user-specified constraints like boundary interpolation, planarity faces, statics, panel size shape, enclosed volume, last, but not least, cost. Our main application is interactive modeling architectural industrial design. approach can be described as guided exploration constraint space whose algebraic structure simplified by introducing auxiliary variables ensuring...

We present a new approach to geometric modeling with developable surfaces and the design of curved-creased origami. represent developables as splines express nonlinear conditions relating developability curved folds quadratic equations. This allows us utilize constraint solver, which may be described energy-guided projection onto manifold, is fast enough for interactive modeling. Further, combined primal-dual surface representation enables robustly quickly solve approximation problems.

Variational interpolation in curved geometries has many applications, so there always been demand for geometrically meaningful and efficiently computable splines manifolds. We extend the definition of familiar cubic spline curves tension, we show how to compute these on parametric surfaces, level sets, triangle meshes, point samples surfaces. This list is more comprehensive than it looks, because includes variational motion design animation, allows treatment obstacles via barrier All...

Motivated by applications in architecture and manufacturing, we discuss the problem of covering a freeform surface single curved panels. This leads to new concept semi-discrete representation, which constitutes link between smooth discrete surfaces. The basic entity are working with is developable strip model. It equivalent quad mesh planar faces, or conjugate parametrization surface. We present B-spline based optimization framework for efficient computing D-strip models. In particular study...

The geometric challenges in the architectural design of freeform shapes come mainly from physical realization beams and nodes. We approach them via concept parallel meshes, present methods computation optimization. discuss planar faces, controlled height, node geometry, multilayer constructions. Beams constant height are achieved with new type edge offset meshes. Mesh parallelism is also main ingredient a novel discrete theory curvatures. These applied to construction quadrilateral,...

The geometric challenges in the architectural design of freeform shapes come mainly from physical realization beams and nodes. We approach them via concept parallel meshes, present methods computation optimization. discuss planar faces, controlled height, node geometry, multilayer constructions. Beams constant height are achieved with new type edge offset meshes. Mesh parallelism is also main ingredient a novel discrete theory curvatures. These applied to construction quadrilateral,...