Ghosh, P., and Mudur, S., "The Brush-Trajectory Approach to Figure Specification: Some Algebraic-Solutions," ACM Transactions on Graphics , Vol. 3, No. 2, pp. 110--134, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the exact sweep boundary consists of high degree algebraic surface patches, the ray intersection computation essentially considers only the general sweep restricted to the one dimensional ray and determines its extreme end points. Related with the computation of general sweep, Ghosh and Mudur [12] suggested an algorithm to compute the closed form analytic curve equation of brush trajectory boundary for brushes with dynamically changing shapes. However, there are two limitations in their algorithm. First, the derived curve equations are complex analytic equations, and thus it would not be ....

Ghosh, P., and Mudur, S., "The Brush-Trajectory Approach to Figure Specification: Some Algebraic-Solutions," ACM Transactions on Graphics , Vol. 3, No. 2, pp. 110--134, 1984.

....shape control parameters) makes the control of flexible brush stroke shapes relatively easy and intuitive. This in turn makes the coordinated motion control of brush strokes relatively easy, too. There are also other related works on modeling brush strokes using different methods. Ghosh and Mudur [11] derived analytic solutions to describe the outline of a brush trajectory. Ahn, Kim, and Lim [2] considered the brush trajectory generated by an arbitrary shape brush which changes its shape dynamically while it moves along an arbitrary plane curve trajectory. They approximate the boundary of such ....

Ghosh, P., and Mudur, S., "The Brush-Trajectory Approach to Figure Specification: Some Algebraic-Solutions," ACM Transactions on Graphics, Vol. 3, No. 2, pp. 110--134, 1984.

....x y Fig. 1.1. a) Offset and (b) convolution of planar objects Offset and convolution computations are classic operations in CAD CAM, which can be used in various interesting geometric applications such as NC machining [8, 18] motion planning [3, 17, 28] character font and brush stroke design [14, 15], blending [31] and shape transformation [22] The exact offset and convolution curves of planar algebraic curves are algebraic, but not rational. Moreover, they have very high algebraic degree [12, 19, 23] For example, the offset of a cubic B ezier curve has an algebraic degree of 10 [12] ....

....Curves 11 3. Convolution Approximation Methods 3. 1 Planar Convolution Curve Convolution is a classic operation which has been used as a tool for computing collision free paths in robot motion planning [3, 17, 28] Moreover, the convolution operation has applications in character font design [14, 15], offset and rounding [31] and shape transformation [22] a) b) c) d) C1 C2 C 2 C 1 x y GammaC 2 C 1 C 1 ( GammaC 2 ) Fig. 3.1. Convolution and C space obstacle Given two regular parametric curves: C 1 (t) x 1 (t) y 1 (t) t 0 t t 1 , and C 2 (s) x 2 (s) y 2 (s) s ....

[Article contains additional citation context not shown here]

Ghosh, P., and Mudur, S.P. (1984): The brush-trajectory approach to figure specification: Some algebraic-solutions. ACM Trans. on Graphics, 3(2):110--134.

....in terms of pen and or brush sweeps is quite natural since it simulates the way of human writing characters. The sweep computations have various other applications in graphic arts, science, and engineering (see [1] for a detailed summary on related problems and previous works) Ghosh and Mudur [6] suggested an (approximation) algorithm to compute the closed form analytic curve equation of brush trajectory boundary for brushes with dynamically changing shapes. However, the derived curve equations are complex analytic equations, and thus it is not easy to implement efficient and robust ....

Ghosh, P.K., and Mudur, S.P., (1984), "The Brush - Trajectory Approach to Figure Specification: Some Algebraic - Solutions," ACM Trans. Graphics, Vol. 3, No. 2, pp. 110--134.

....applications are mostly concerned with rigid moving objects, there are increasing demands in computer graphics and other related areas for modeling the general sweeps of moving objects with flexible shapes. An immediate application of the general sweep is in the design of brush strokes [1, 9]. See [1] for a detailed summary on related problems and previous works. In this paper, we suggest an algebraic algorithm to compute the exact general sweep boundary of a 2D curved object which moves in its own xy plane along a parametric curve trajectory while changing its shape parametrically. ....

Ghosh, P., and Mudur, S., (1984), "The Brush-Trajectory Approach to Figure Specification: Some Algebraic-Solutions," ACM Transactions on Graphics, Vol. 3, No. 2, pp. 110--134.

....O 2 x y Fig. 1. a) Offset and (b) convolution of planar objects Offset and convolution computations are classic operations in CAD CAM, which can be used in various interesting geometric applications such as NC machining [8, 17] motion planning [3, 16, 27] character font and brush stroke design [13, 14], blending [30] and shape transformation [21] The exact offset and convolution curves of planar algebraic curves are algebraic, but not rational. Moreover, they have very high algebraic degree [12, 18, 22] For example, the offset of a cubic B ezier curve has an algebraic degree of 10 [12] ....

....curves. 3 Convolution Approximation Methods 3. 1 Planar Convolution Curve Convolution is a classic operation which has been used as a tool for computing collision free paths in robot motion planning [3, 16, 27] Moreover, the convolution operation has applications in character font design [13, 14], offset and rounding [30] and shape transformation [21] a) b) c) d) C 1 C 2 C 2 C 1 x y GammaC 2 C 1 C 1 ( GammaC 2 ) Fig. 8. Convolution and C space obstacle Given two regular parametric curves: C 1 (t) x 1 (t) y 1 (t) t 0 t t 1 , and C 2 (s) x 2 (s) y 2 (s) s 0 s ....

[Article contains additional citation context not shown here]

Ghosh, P., and Mudur, S.P.: The brush-trajectory approach to figure specification: Some algebraic-solutions. ACM Trans. on Graphics, 3 (1984) 110--134

....in a compact form suitable for direct input to rendering systems like PostScript(R) in 2D and Renderman(R) in 3D. Keywords: Swept objects, sweep rules, boundary evaluation, volume modelling, region modelling, body modelling, pen stroke modelling. 1. Introduction Pen stroke modelling in 2D[1,2] and body modelling in 3D[3] are typical examples of spine based modelling. Designing such regions volumes as a spine with a generator contour sweeping over it has the advantages of not only providing a more natural way of modelling but also of effectively parameterising the essential geometric ....

P.K. Ghosh, S. P. Mudur, The brush-trajectory approach to figure specification: some algebraic solutions, ACM Tr. on Computer Graphics 3 (1984).

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