Yi-Jun Yang

A rational extension of Piegl's method for filling n-sided holes

N-sided hole filling plays an important role in vertex blending. To deal with the case that the corner is surrounded by rational surfaces (i.e. NURBS surfaces), an algorithm to fill n-sided holes with @e- G^1 continuous NURBS patches that interpolate the given boundary curves and approximate the given cross-boundary derivatives is presented based on Piegls method. The NURBS surfaces joining along inner or boundary curves have normal vectors that do not deviate more than the user-specified angular tolerance @e. The boundaries as well as cross-boundary derivatives can all be NURBS curves. No restrictions are imposed on the number of boundary curves, and the cross-boundary derivatives can be specified independently.

Optimal parameterizations of bézier surfaces

The presentation of Bezier surfaces affects the results of rendering and tessellating applications greatly. To achieve optimal parameterization, we present two reparameterization algorithms using linear Mobius transformations and quadratic transformations, respectively. The quadratic reparameterization algorithm can produce more satisfying results than the Mobius reparameterization algorithm with degree elevation cost. Examples are given to show the performance of our algorithms for rendering and tessellating applications.

G1 continuous approximate curves on NURBS surfaces

Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a parabola approximation method based on the cubic reparameterization of rational Bezier surfaces, which generates G1 continuous approximate curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the approximate curve and the exact curve is controlled under the user-specified tolerance. Examples are given to show the performance of our algorithm. Highlights? We present a method to generate G1 continuous approximate curves on NURBS surfaces. ? We give the cubic reparameterizations of rational Bezier surfaces. ? The Hausdorff distance between the approximate and exact curves is controlled. ? The approximate curve is lying completely on the NURBS surface. ? Iso-parameter curves of the reparameterized surfaces constitute the resulting curve.

An algorithm for tetrahedral mesh generation based on conforming constrained Delaunay tetrahedralization

An unstructured previous termtetrahedral mesh generation algorithmnext term for 3D model with constraints is presented. To automatically generate a previous termtetrahedral meshnext term for model with constraints, an advancing front previous termalgorithmnext term is presented previous termbased on conforming constrained Delaunay tetrahedralizationnext term (CCDT). To reduce the number of visibility tests between vertices with respect to model faces as well as the computation of previous termconstrained Delaunaynext term tetrahedra, a sufficient condition for DT (previous termconstrained Delaunay tetrahedralizationnext term whose simplexes are all previous termDelaunay)next term existence is presented and utilized coupled to uniform grid and advancing front techniques in our previous termalgorithm. The meshnext term generator is robust and exhibits a linear time complexity for mechanical models with uniform density distribution.

Optimizing equiareality of NURBS surfaces using composite Möbius transformations

The equiareality of NURBS surfaces greatly affects the results of visualization and tessellation applications, especially when dealing with extruding and intruding shapes. To obtain more equiareal parameterizations of NURBS surfaces than the Mobius based method, an optimization algorithm is presented in this paper based on the more flexible composite reparameterization functions. For fixed knots, the optimal composite reparameterization can be obtained using the Levenberg-Marquardt method. For a given tolerance, a uniform subdivision scheme is interleaved with the optimization procedure and this process finishes until the change of the equiareal deviation energy is less than the given tolerance. Examples are given to show the performance of our algorithm for visualization and tessellation applications.

Constrained delaunay triangulation using delaunay visibility

An algorithm for constructing constrained Delaunay triangulation (CDT) of a planar straight-line graph (PSLG) is presented. Although the uniform grid method can reduce the time cost of visibility determinations, the time needed to construct the CDT is still long. The algorithm proposed in this paper decreases the number of edges involved in the computation of visibility by replacing traditional visibility with Delaunay visibility. With Delaunay visibility introduced, all strongly Delaunay edges are excluded from the computation of visibility. Furthermore, a sufficient condition for DT (CDT whose triangles are all Delaunay) existence is presented to decrease the times of visibility determinations. The mesh generator is robust and exhibits a linear time complexity for randomly generated PSLGs.

A two-view VR shooting theater system

In traditional shooting theater system, only one single scene image can be presented to all the players, and the interaction based on simulation guns is limited. In this paper, we describe a novel shooting theater system for freely moving players, which is equipped with two-view projecting system, individual surround-stereo earphone and user-customized simulation gun. To provide friendly user interaction, a new-designed strategy of simulation gun is introduced. In the end, a tennis game system is given to show the extensibility and practicability of our system.

Colon Flattening by Landmark-Driven Optimal Quasiconformal Mapping

In virtual colonoscopy, colon conformal flattening plays an important role, which unfolds the colon wall surface to a rectangle planar image and preserves local shapes by conformal mapping, so that the cancerous polyps and other abnormalities can be easily and thoroughly recognized and visualized without missing hidden areas. In such maps, the anatomical landmarks (taeniae coli, flexures, and haustral folds) are naturally mapped to convoluted curves on 2D domain, which poses difficulty for comparing shapes from geometric feature details. Understanding the nature of landmark curves to the whole surface structure is meaningful but it remains challenging and open. In this work, we present a novel and effective colon flattening method based on quasiconformal mapping, which straightens the main anatomical landmark curves with least conformality (angle) distortion. It provides a canonical and straightforward view of the long, convoluted and folded tubular colon surface. The computation is based on the holomorphic 1-form method with landmark straightening constraints and quasiconformal optimization, and has linear time complexity due to the linearity of 1-forms in each iteration. Experiments on various colon data demonstrate the efficiency and efficacy of our algorithm and its practicability for polyp detection and findings visualization; furthermore, the result reveals the geometric characteristics of anatomical landmarks on colon surfaces.

Surface Matching and Registration by Landmark Curve-Driven Canonical Quasiconformal Mapping

This work presents a novel surface matching and registration method based on the landmark curve-driven canonical surface quasiconformal mapping, where an open genus zero surface decorated with landmark curves is mapped to a canonical domain with horizontal or vertical straight segments and the local shapes are preserved as much as possible. The key idea of the canonical mapping is to minimize the harmonic energy with the landmark curve straightening constraints and generate a quasi-holomorphic 1-form which is zero in one parameter along landmark and results in a quasiconformal mapping. The mapping exists and is unique and intrinsic to surface and landmark geometry. The novel shape representation provides a conformal invariant shape signature. We use it as Teichmuller coordinates to construct a subspace of the conventional Teichmuller space which considers geometry feature details and therefore increases the discriminative ability for matching. Furthermore, we present a novel and efficient registration method for surfaces with landmark curve constraints by computing an optimal mapping over the canonical domains with straight segments, where the curve constraints become linear forms. Due to the linearity of 1-form and harmonic map, the algorithms are easy to compute, efficient and practical. Experiments on human face and brain surfaces demonstrate the efficiency and efficacy and the potential for broader shape analysis applications.

An algorithm to improve parameterizations of rational Bézier surfaces using rational bilinear reparameterization

The parameterization of rational Bezier surfaces greatly affects rendering and tessellation results. The uniformity and orthogonality of iso-parametric curves are two key properties of the optimal parameterization. The only rational Bezier surfaces with uniform iso-parametric curves are bilinear surfaces, and the only rational Bezier surfaces with uniform and orthogonal iso-parametric curves are rectangles. To improve the uniformity and orthogonality of iso-parametric curves for general rational Bezier surfaces, an optimization algorithm using the rational bilinear reparameterizations is presented, which can produce a better parameterization with the cost of degree elevation. Examples are given to show the performance of our algorithm for rendering and tessellation applications.