Bicubic parametric patches on tongue

In this case, the polynomials are functions of two parameters, u and v. To create smooth hull shapes, ancient ship builders would drive pegs into the ground, and then lay down a very large thin flexible strip of wood the spline that would be forced into a curve by the position of the pegs. Therefore the resulting shape and texturing depend on the actual mapping, i. New geometric continuity solution of parametric surfaces. I learned how to calculate bicubic surfaces by reading the course material that ken perlin so kindly provides.

Filling polygonal holes with bicubic patches sciencedirect. The proposed new modification of the hermite bicubic patch, the hspatch, is a result of additional restriction put on the hermite bicubic patch formulation the diagonal and antidiagonal curves are of degree 3. Bicubic patch bounds 97 this is a bicubic equation for u and w and is relatively easy to handle. A coons patch named after steven anson coons, 19121979 is a bicubic parametric surface formed by four corner points, eight tangent vectors two vectors in the u and w directions, respectively, at each of the four corners, and four twister vectors at the respective four corner points, as shown in figure 2. Lecture outline more on curves and parametric bicubic. We propose an algorithm for visually approximating catmullclark subdivision surfaces, possibly with boundaries, using a collection of bicubic patches one for each face of a quadmesh. By taking a set of four cubic curves with parameter s and using these four curves to generate a set of four control points for any given value of s, and then using these control points to define a parametric curve with parameter t we can generate a surface called a bicubic patch. Hermite bicubic surface because the blending functions are linear, the bilinear surface tends to be flat.

A new modification of the hermite cubic rectangular patch is proposed the s patch, which is based on the requirement that diagonal curves must be of degree 3 instead of degree 6 as it is in the case of the hermite patch. We contend approximating the surface with patches that are in onetoone correspondence with the faces of the coarsest base mesh is best. A 3d parametric tongue model for animated speech king. Keywords parametric surface, geometric modeling, computer.

The goal is to go from curves in space to curved surfaces in space. The points in the patch corresponding to the corners of the deformed unit square coincide with four of the control points. Improved bicubic patchnatural surface counterpart of the. The graphics state maintains two 4x4 matrices that define the bicubic patch basis matrices. Patches can also be rational or nonrational depending on whether the control points are x,y,z or x,y,z,w. In this paper the problem of blending parametric surfaces using subdivision patches is discussed. The method and system of include transforming only the control points of the. The paper considers a limitation in the construction of the bicubic patch and introduces a generalization, the improved bicubic patch. Generally, the most common use of bezier surfaces is as nets of bicubic patches where m n 3. The main result is that the improved bicubic patch is, in the context of shape definition, the natural surface counterpart of the parametric cubic segment. Approximating catmullclark subdivision surfaces with. Madhusudhan, department of mechanical engineering, iit delhi. It is used to calculate cutter offsets for threedimensional nc programming to machine surfaces, volume calculations, and shading of a surface model. This mapping is a cubic polynomial in for each fixed and a cubic polynomial in for each fixed.

Parametric surfaces our discussions on parametric cubic curves can be generalized to parametric bicubic surfaces. A twodimensional bicubic hermite patch is a smooth map from the unit square to a region. In general, a bezier curve in two dimensions is defined by four control points. Bicubic patches the concept of parametric curves can be extended to surfaces the cubic parametric curve is in the form of where control points, m is the basis. Thus if the patch happens to be planar and tilted with respect to the coordinate axes, the transformation produces a new set of coordinates such that the plane of the patch is parallel to one of the coordinate planes. Contributions we propose an algorithm for visually approximating catmullclark subdivision surfaces, possibly with boundaries, using a collection of bicubic patches one for each face of a quadmesh. Each patch is defined by blending control points same ideas as parametric curves. The model is capable of representing tongue shapes during the production of english vowels and consonants as well as general motion of the tongue. Approximate with polygons draw polygons how do we specify a surface. Patches can be either uniform or nonuniform contain different knot values. If it happens that the surface patch is a nonparametric bicubic, that is x3 vx,a vx, x. Patchy provides an easytouse bicubic patch for 3d graphics in the processing programming environment. This paper presents a new approach to computation of geometric continuity for parametric bi cubic patches, based on a simple mathematical reformulation which leads to simple additional conditions to be applied in the patching computation.

The geometry of a single bicubic patch is thus completely defined by a set. The proposed new modification of the hermite bicubic patch, the hs patch, is a result of additional restriction put on the hermite bicubic patch formulation the diagonal and antidiagonal curves are of degree 3. Part of patchy is based on his code, and i am very grateful for it. Parametric surface patch xu,v describes a point in space for any given u,v pair u,v each range from 0 to 1 parametric curves for fixed u 0, have a v curve xu 0,v for fixed v 0, have a u curve xu,v 0 for any point on the surface, there are a pair of parametric curves through that point cse 167, winter 2020 11 0 1 1 u. These are hard to detect on a parametric representation. Bicubic surfaces thursday, december 12, 20 parametric bicubic surfaces.

However, a bezier surface does not generally pass through its other control points. This summary will focus on parametric bezier surface patches. Parametric models control tongue deformation with several parameters that represent the meaningful shape attributes of the tongue 39, 40. Explicit, implicit, parametric how do we approximate a surface. Parametric bicubic surfaces cubic polynomials are also used for piecewise interpolation of sets of points on a surface. This requirement leads to a new hermite based bicubic foursided patch with 12 control points and another 4 control points, i. We want to define we want to define smooth surfaces too. Bicubic surface patch with 4 e 4 control points note. Each bicubic surface is defined by sixteen control points and bounded by four boundary curves, and each boundary curve is formed by boundary box of line segments formed between four of the control points. Blending parametric patches with subdivision surfaces. Computer graphics 16 curves and surfaces 1 tom thorne slides courtesy of taku komura. Synthetic surfaces aml710 cad lecture 18 parametric representaion in parametric surfaces a vector valued function pu,v of two variables is used as follows.

So if adjacent meshes share edge points, the patches will line up. Aspects for rendering bicubic surfaces of an object on a computer system are disclosed. This requirement leads to a new hermite based bicubic foursided patch. A surface may be one patch or constructed using several patches. Talk given at the conference on applications of computer algebra aca 2007, approximate algebraic computation session july, 2007, oakland university, rochester, mi. A new approach, named removingboundary, is presented to generate piecewisesmooth subdivision surfaces through discarding the outmost quadrilaterals of the open meshes derived by each subdivision step. Several theoretical studies and also algorithms have aimed to delimit zones in the u,v plane where they could not appear. The geometry of a single bicubic patch is thus completely defined by a set of 16 control points. A bicubic patch is the real twodimensional part of x. It is still desirable to eliminate as many patches as possible by simpler means. Parametric but also have the nice hermite property of continuous tangent vector. Bicubic parametric patches a bicubic hertmite patch is described in a matrix form for the coordinate as. A similar definition holds for a twodimensional patch on a surface in, with an additional function.