ガウス分布関数を応用した座標系の歪曲と幾何学模様の生成 Distortion of Coordinate System by Gauss'Distribution Surface and Creation of Geometric Figures
This paper described an algorithm to transform part of geometric figures created by a function continually using Gauss' distribution function, and its application. This algorithm will show new technique to get transformation mappings of geometric figure.<BR>The fundamental way of thinking in this algorithm is not to transform geometric figures on an orthogonal coordinate system, but to distort the system continualy and partially using Gauss' distribution function, and to produce geometric figures on the coordinate system distorted.<BR>In this paper, first, I show three fundamental conversion forms to get orthogonal coordinate system distorted continualy and partially using Gauss' distribution surface. The first method is to do coordinate transformation of a point on a plane, using a change rate of height of Gauss' distribution surface (partial differential coefficient) as revision value. The second conversion form is the projection of a point on Gauss' distribution surface form a fixed point, to convert a coordinate of a point on a plane. And the last method is to convert coordinate of a point rotationally, using height of Gauss' distribution surface as angle of rotaion on a plane.<BR>The next discussion shows how geometric figures on orthogonal coordinate system are transfigured on the distorted coordinate system, and characteristics and application of these methods.<BR>By this, we can have technique to create various and unique geometric figures, transforming part of geometric figure continually from a simple general idea of distortion of coordinate system.
図学研究 32(4), 29-38, 1998-12-01