GPU accelerated parameter curve arc length calculation and arc length parameterization method

Abstract

The invention discloses a GPU accelerated parameter curve arc length calculation and arc length parameterization method, and relates to the field of computer aided design. The GPU accelerated parameter curve arc length calculation and arc length parameterization method is friendly to a data storage mode and a GPU data access mode, small in instruction divergence rate and capable of reducing time consumption. The method comprises the following steps: inputting the number of parameter curves, the number of interval sections of each parameter curve and curve parameters; equally dividing parametercell sections; constructing an arc length table; taking out the curve arc length from the arc length table; inputting an arc length value of arc length parameterization to be solved and a number of acurve where the arc length value is located; determining a search interval where the arc length is located; binary tree traversal backtracking-accelerated depth-first search based on binary bit operation is used, and the length of a search interval is reduced to be not larger than an error range specified by a user; and outputting the midpoint of the final search interval as a parameter corresponding to the arc length. And the method has higher parallelism and is more suitable for the SIMT architecture of the GPU.

Description

technical field [0001] The invention relates to the field of computer-aided design, in particular to a GPU-accelerated parameter curve arc length calculation and arc length parameterization method. Background technique [0002] Arc length calculation and arc length parameterization of parametric curves are widely used in motion control, path planning and other problems. [0003] The arc length function of a parametric curve C(u) is defined as starting from the minimum parameter value u 0 Up to the parameter t, the point-by-point tangent of the curve is the integral of the modulus length of the first-order derivative vector, that is, the arc length formula For the task in the opposite direction, the arc length a is given, and the corresponding parameter t is obtained by the inverse function of the arc length function, that is, t=A -1 (a), called arc length parameterization. [0004] Due to the complex form of the parametric curve, its arc length formula often cannot be re...

AI Technical Summary

Problems solved by technology

[0007] The traditional CPU method uses a recursive method to calculate the arc length and solve the parameterization of the arc length. Due to the high amount of calculation, this method requires a long calculation time, and its method is compared with the single instruction multiple thread (SIMT) architecture of the GPU. , has many disadvantages such as large function call overhead, high instruction divergence rate, and a large amount of local storage space

In addition, the arc length table in the method is dynamically constructed, and its storage space needs to be dynamically allocated and released at runtime, which is expensive in the GPU, so it is not suitable for direct porting to the GPU

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