J. Hoschek and D. Lasser. Fundamentals of Computer Aided Geometric Design. AK Peters, Wellesley, MA, 1993. Home/Search Document Not in Database Summary Related Articles Check |
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Geometries for CAGD - Pottmann, Leopoldseder (Correct)
....for the introduction of the full class of rational curves and surfaces into CAGD. The most basic algorithm for Bzier curves, de Casteljau s algorithm, is for degree 2 equivalent to Steiner s generation of a conic with help of two projective lines, or more precisely, ranges of points (see [25,26,39]) However, not only quadratic Bzier curves are deeply rooted in projective geometry. The same holds for the full class of rational Bzier curves [18] The corresponding concept in projective geometry is that of rational normal curves [6] These are rational curves c of degree n which span ....
....for rational Bzier triangles have been introduced by G. Albrecht [1] Projective geometry enters many algorithms for rational curves and surfaces, such as reparameterization, degree elevation and shape modification. For those topics, the reader is referred to chapter of this handbook and to [25,26,39,72] and the references therein. 1.3. Duality and Dual Representation The Bzier representation of a rational curve expresses the polynomial homogeneous parametrization c(t)t in terms of the Bernstein polynomials. Then the coefficients have the remarkable geometric meaning of control points with a ....
Hoschek, J., Lasser, D.: Fundamentals of Computer Aided Geometric Design. A. K. Peters, Wellesley, MA 1993.
Hierarchical Multiresolution Reconstruction of Shell Surfaces - Bajaj, Xu (Correct)
....to represent the shell will not be accurate (see e.g. Figure 5.3 and Figure 6.2) Therefore, two boundaries of the shell as well as surfaces in between need to be constructed. Of course, one could solve the proposed geometric modeling problem by using classical or existing methods (see, e.g. [9, 15, 21]) of parametric surface splines to construct individual boundary surfaces as well as mid surfaces of the shell boundaries. However, the independent construction of each surface not only increases tremendously the space and time costs, but also fails to guarantee that these surfaces are always ....
J. Hoschek and D. Lasser. Fundamentals of Computer Aided Geometric Design. A. K. Peters, 1993.
On the Generation of Smooth Three-Dimensional Rigid Body.. - Zefran, Kumar, Croke (1995) (2 citations) (Correct)
.... and painting where a teaching process is employed to record intermediate positions and the final trajectory is obtained by interpolation [2] Similarly, in computer animation it is necessary to generate a smooth trajectory passing through a set of key frames specifying positions and orientations [3]. In this case, smoothness is required to obtain realistic motions or motions that look natural. There are several factors that need to be considered when developing a trajectory planning method. It is desirable that the trajectories are independent of the choice of coordinates for the space. ....
J. Hoschek and D. Lasser, Fundamentals of Computer Aided Geometric Design, AK Peters, 1993.
Taylor Models and Affine Arithmetics - Towards a More.. - Bühler (2001) (Correct)
....(u; v; s; t) 2 I J As there is no restriction on the type of surfaces, the exact solution of this problem can be determined only in a few special cases, e.g. low degree polynomial or rational surfaces. 5. 2 Existing Solutions Among the great variety of existing solutions (for a survey see e.g. [16]) two approaches turn out to be predominant: subdivision and marching algorithms. Marching algorithms are fast, but require an expensive preprocessing, they fail if the problem is ill conditioned and it is hard to determine if all parts of the intersection where detected. Subdivision algorithms ....
J. Hoschek and D. Lasser. Fundamentals of Computer Aided Geometric Design. A K Peters, 1993.
A Multiresolution Framework for Variational Subdivision - Kobbelt, Schröder (1998) (13 citations) (Correct)
....transformations are easy to implement and efficient enough for interactive applications. Introduction A basic component of many algorithms in shape design is the efficient construction of interpolating curves, given some set of data points. Many techniques have been developed for this purpose [18, 13], the most widely used ones being based on piecewise polynomials. However, to obtain high quality curves differentiability is usually not sufficient but optimality with respect to some fairness measure is required as well [3, 26] Applications such as level of detail rendering [25] data ....
....and the recently introduced variational subdivision setting. We extended the latter to the non uniform parameterization setting. It is well known in the CAGD community Figure 5: Curvature distribution of the cubic splines (left) compared to minK 3 (p i ) 2 curves (right) see for example [18]) that both variational settings and non uniform settings are very important in practice, giving a much richer foundation on which to build smooth curves. We gave a simple example hinting at some of the differences between the different variational energy measures and the effects of non uniform ....
HOSCHEK,J.,AND LASSER,D.Fundamentals of Computer Aided Geometric Design. AK Peters, 1993.
An Efficient, Geometric Approach to Rigid Body Motion.. - Belta, Kumar (2000) (Correct)
....the near optimality of the projected curves. 1 Introduction We address the problem of finding a smooth motion that interpolates a given set of positions and orientations. This problem finds applications in robotics and computer graphics. The problem is well understood in Euclidean spaces [4, 7], but it is not clear how these techniques can be generalized to curved spaces. There are several issues that need to be addressed, particularly on non Euclidean spaces. It is desirable that the computational scheme be independent of the description of the space and invariant with respect to the ....
J. Hoschek and D. Lasser. Fundamentals of Computer Aided Geometric Design. AK Peters, 1993.
Macro-Elements and Stable Local Bases for Splines on.. - Lai, Schumaker (1999) (2 citations) (Correct)
....the equation c mmm B 3m mmm (v) s(v) Gamma X =3m ( 6= m;m;m) c B 3m (v) Note that B 3m mmm (v) is bounded below by a constant depending on in view of Lemma 2.2, and so c mmm can also be stably computed. We can now apply the de Casteljau algorithm (cf. 4] [5]] to subdivide the polynomial into a spline of degree 3m on the Powell Sabin split of e T . It is well known that this is a stable process. Finally, we transfer the computed coefficients back to the B net for the spline s. To compute the dimension of Sm (4 v ) we observe that #M = 3 3m ....
Hoschek, J., Lasser, D., Fundamentals of Computer Aided Geometric Design, A. K. Peters (Boston MA), 1993.
Interpolation Schemes for Rigid Body Motions - Zefran, Kumar (1997) (3 citations) (Correct)
....in welding and painting) computer graphics (animation, interpolation of motion through a set of key frames) and computer aided geometric design (interactive interpolation schemes for design) and has recently received considerable attention. The problem is well understood in Euclidean spaces [6, 9], but it is not clear how these techniques can be generalized to curved spaces. There are several issues that need to be addressed, particularly on non Euclidean spaces. It is desirable that the computational scheme be independent of the description of the space and invariant with respect to the ....
J. Hoschek and D. Lasser. Fundamentals of Computer Aided Geometric Design. AK Peters, 1993.
Int. Conf. on Advanced Robotics (ICAR'97), Monterey, CA, July.. - Path Planning For (Correct)
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J. Hoschek and D. Lasser. Fundamentals of Computer Aided Geometric Design. AK Peters, Wellesley, MA, 1993.
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J. Hoschek and D. Lasser. Fundamentals of Computer Aided Geometric Design. AK Peters, Wellesley, MA, 1993.
Direct Haptic Rendering of Sculptured Models - Thompson II, Johnson, Cohen (1997) (16 citations) (Correct)
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Hoschek, J., and Lasser, D., 1993. Fundamentals of Computer Aided Geometric Design. AK Peters.
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J Hoschek and D Lasser. Fundamentals of Computer Aided Geometric Design. Wellesley, 1993.
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Hoschek J., Lasser D., Fundamentals of Computer Aided Geometric Design,A.K.Pe- ters, (1993). 27
A Case Study on Interactive Exploration and Guidance Aids for .. - Stoev, Straßer (2001) (1 citation) (Correct)
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Joseph Hoschek and Dieter Lasser. Fundamentals of Computer Aided Geometric Design. A. K. Peters, 1993.
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J. Hoschek and D. Lasser. Fundamentals of Computer Aided Geometric Design. A K Peters, 1993.
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Hoschek J., Lasser D.: Fundamentals of Computer Aided Geometric Design. A.K. Peters (1993).
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Hoschek, J. and D. Lasser, Fundamentals of Computer Aided Geometric Design, A. K. Peters, Boston, 1993.
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Hoschek, J. and Lasser, D., Fundamentals of Computer Aided Geometric Design, A. K. Peters, Wellesley, MA, 1993, Translated by L. L. Schumaker.
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J.Hoschek, D.Lasser, Fundamentals of Computer Aided Geometric Design, A.K.Peters (1993).
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J. Hoschek and D. Lasser, Fundamentals of Computer Aided Geometric Design. Wellesley, MA: A. K . Peters, 1993.
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