Topic
Bicubic interpolation
About: Bicubic interpolation is a research topic. Over the lifetime, 3348 publications have been published within this topic receiving 73126 citations.
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TL;DR: It is shown that for cubic splines or bicubic patches, accurate tool motion can be generated by a fast DDA-like (Digital Differential Analyser) digital integration scheme, which reduces integration to successive additions.
Abstract: A method is proposed for generating tool centre paths with an accuracy equal to the resolution of the machine tool. The method exploits the properties of Bertrand curves and surfaces, to generate tool motion which secures the desired degree of continuity in the machined contour or surface. It is shown that for cubic splines or bicubic patches, accurate tool motion can be generated by a fast DDA-like (Digital Differential Analyser) digital integration scheme, which reduces integration to successive additions. Accuracy is achieved by eliminating the integration error inherent in DDA.
43 citations
TL;DR: A novel 8-bit linear interpolation algorithm was implemented as a CMOS VLSI circuit using a readily available, high-level synthesis tool and results produced were virtually identical to IEEE-format, single-precision, floating-point results.
43 citations
TL;DR: Representations of cubic and bicubic splines are given, combining the advantages of B-splines with the handiness of Bézier technique, suited especially for computer aided geometric design.
Abstract: Representations of cubic and bicubic splines are given, combining the advantages of B-splines with the handiness of Bezier technique. The Bezier points of spline curves and surfaces are found by forming convex combinations of nodes. The given algorithms are suited especially for computer aided geometric design.
43 citations
01 Aug 1987
TL;DR: Two new methods are presented for deriving bicUBic approximations to the shading parameters over a bicubic patch, suitable for both hardware and software implementations.
Abstract: We present several techniques for implementing Phong shading in hardware for bicubic patches. Patches are shaded, not by subdividing into polygons, but by drawing many curves close together leaving no pixel gaps. Each curve is drawn using an adaptive forward difference algorithm which generates the coordinates as well as the shading parameters as cubic functions incrementally evaluated along the curve. The forward difference step size is adaptively adjusted so that it generates approximately one pixel along the curve per forward difference step. The hardware implements Phong shading directly with a surprisingly simple configuration built from general purpose compute units and look-up tables. Two new methods are presented for deriving bicubic approximations to the shading parameters over a bicubic patch. One method uses two Coons patches to approximate the unnormalized N·L, and N·H, and a third Coons patch for N·N, where N is the surface normal, L is the light direction, and H is the direction of maximum highlight. In this case the hardware performs the normalization per pixel. The second method uses two Coons patches to approximate the normalized dot products N·L, and N·H. The method is suitable for both hardware and software implementations.
43 citations
Patent•
01 Jul 2003
TL;DR: In this paper, a reduced multicubic database interpolation method is proposed to map a function and its associated argument into an interpolated value using a database of points, which is then generated as a cubic function using the data points that correspond to vertices of the unit cell.
Abstract: A reduced multicubic database interpolation method is provided. The interpolation method is designed to map a function and its associated argument into an interpolated value using a database of points. The database is searched to locate an interpolation cell that includes the function argument. The interpolation cell is used to transform the function argument to reflect translation of the interpolation cell to a unit cell. The interpolated value is then generated as a cubic function using the data points that correspond to vertices of the unit cell. All of the derivatives in the cubic function are simple and the interpolation accuracy order is higher than first-order.
43 citations