We decompose the problem of the optimal multi-degree reduction of Bézier curves with corners constraint into two simpler subproblems, namely making high order interpolations at the two endpoints without degree re...
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We decompose the problem of the optimal multi-degree reduction of Bézier curves with corners constraint into two simpler subproblems, namely making high order interpolations at the two endpoints without degree reduction, and doing optimal degree reduction without making high order interpolations at the two endpoints. Further, we convert the second subproblem into multi-degree reduction of Jacobi polynomials. Then, we can easily derive the optimal solution using orthonormality of Jacobi polynomials and the least square method of unequally accurate measurement. This method of 'divide and conquer' has several advantages including maintaining high continuity at the two endpoints of the curve, doing multi-degree reduction only once, using explicit approximation expressions, estimating error in advance, low time cost, and high precision. More importantly, it is not only deduced simply and directly, but also can be easily extended to the degree reduction of surfaces. Finally, we present two examples to demonstrate the effectiveness of our algorithm.
We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the ...
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We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples This method has the following three advantages： （1） the pattern is unified; （2） the parameter able to adjust the shape of the transition curve is available; （3） the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.
We present a novel approach for dealing with optimal approximate merging of two adjacent Bezier eurves with G^2-continuity. Instead of moving the control points, we minimize the distance between the original curves an...
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We present a novel approach for dealing with optimal approximate merging of two adjacent Bezier eurves with G^2-continuity. Instead of moving the control points, we minimize the distance between the original curves and the merged curve by taking advantage of matrix representation of Bezier curve＇s discrete structure, where the approximation error is measured by L2-norm. We use geometric information about the curves to generate the merged curve, and the approximation error is smaller. We can obtain control points of the merged curve regardless of the degrees of the two original curves. We also discuss the merged curve with point constraints. Numerical examples are provided to demonstrate the effectiveness of our algorithms.
The paper discusses computergraphics applications in space research, motion picture and commercial film industry. Advantages of 2-D and 3-D computergraphics are outlined along with production requirements of compute...
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ISBN:
(纸本)0444876170
The paper discusses computergraphics applications in space research, motion picture and commercial film industry. Advantages of 2-D and 3-D computergraphics are outlined along with production requirements of computergraphics in Japan.
These tutorial notes will explore a number of the most critical issues of concern to the visual arts educator and suggest areas of program specialization. Critical issues in program planning, structure, and content ar...
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ISBN:
(纸本)0941514072
These tutorial notes will explore a number of the most critical issues of concern to the visual arts educator and suggest areas of program specialization. Critical issues in program planning, structure, and content are explored in the context of rapidly changing technologies and applications. A description is also given of one particularly effective structural framework for developing computergraphics curricula which has been field tested for several years at Sheridan computer graphics laboratory.
Poisson disk sampling has been widely used in many applications such as remeshing, procedural texturing, object distribution, illumination, etc. While 2D Poisson disk sampling is intensively studied in recent years, d...
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Poisson disk sampling has been widely used in many applications such as remeshing, procedural texturing, object distribution, illumination, etc. While 2D Poisson disk sampling is intensively studied in recent years, direct Poisson disk sampling on 2-manifold surface is rarely covered. In this paper, we present a novel framework which generates approximate Poisson disk distribution directly on mesh, a discrete representation of 2-manifold surfaces. Our framework is easy to implement and provides extra flexibility to specified sampling issues like feature-preserving sampling and adaptive sampling. We integrate the tensor voting method into feature detection and adaptive sample radius calculation. Remeshing as a special downstream application is also addressed. According to our experiment results, our framework is efficient, robust, and widely applicable.
Rendering large-scale forest scenes in real-time is a challenging problem, since the geometric complexity is far beyond the capabilities of current graphics hardware. In this paper, we propose a novel approach that ad...
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Rendering large-scale forest scenes in real-time is a challenging problem, since the geometric complexity is far beyond the capabilities of current graphics hardware. In this paper, we propose a novel approach that adopts a dynamic quad stream residing on GPU buffers for view-dependent forest rendering. The incremental quad stream updating process is well-suited to the massively parallel architecture of the GPU pipeline, and it requires no continuous data exchange between CPU and GPU. The implementation of the algorithm is quite straightforward. Despite its simplicity, the algorithm achieves good performance with low memory, storage, and CPU costs.
This paper describes a new and fast method for reconstructing a 3D computerized model from a cloud of points sampled from the object's surface. The proposed method aggregates very large scale 3D scanning data into...
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This paper describes a new and fast method for reconstructing a 3D computerized model from a cloud of points sampled from the object's surface. The proposed method aggregates very large scale 3D scanning data into a Hierarchical Space Decomposition Model (HSDM), realized by the Octree data structure. This model can represent both the boundary surface and the interior volume of an object. Based on the proposed volumetric model, the boundary reconstruction process becomes more robust and stable with respect to sampling noise. The hierarchical structure of the proposed volumetric model enables data reduction, while preserving critical geometrical features and object topology. As a result of data reduction, the execution time of the reconstruction process is significantly reduced. Moreover, the proposed model naturally allows multiresolution boundary extraction, represented by a mesh with regular properties. The proposed surface reconstruction approach is based on Connectivity Graph extraction from HSDM, and facet reconstruction. This method's feasibility will be presented on a number of complex objects.
To take full advantage of colour in producing visually effective images, a good interface between the user and the system is needed that will allow for the easy selection of colours. Interactive manipulation, using in...
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To take full advantage of colour in producing visually effective images, a good interface between the user and the system is needed that will allow for the easy selection of colours. Interactive manipulation, using instantaneous colour updating as the feedback mechanism is, of course, well suited for many applications since the trial and error process involved in selecting colours is made continuous. Hence a colour matching experiment using a raster computergraphics system is being conducted at the University of Waterloo to determine which of a number of colour spaces and interaction techniques are most effective in building a user interface for interactive colour manipulation. This paper describes the experiment and reports some preliminary results.
Interactive systems for defining, manipulating and rendering curves and surfaces have been implemented based on a variety of mathematical techniques including B-spline and Beta-spline representations. The talk address...
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Interactive systems for defining, manipulating and rendering curves and surfaces have been implemented based on a variety of mathematical techniques including B-spline and Beta-spline representations. The talk addresses the underlying mathematics, numerical properties, efficient techniques for rendering, shading and texturing methods, and ergonomic issues regarding the interactive manipulation of the curves and surfaces through their representations.
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