×

Three-dimensional object movement and transformation processing apparatus for performing movement and transformation of an object in a three-diamensional space

  • US 5,581,665 A
  • Filed: 10/26/1993
  • Issued: 12/03/1996
  • Est. Priority Date: 10/27/1992
  • Status: Expired due to Term
First Claim
Patent Images

1. A three-dimensional object movement and transformation processing apparatus, comprising:

  • shape storing means for storing shapes of a plurality of objects including a first object and a second object which are prescribed in shape prescription coordinate systems of a three-dimensional space;

    Mwo matrix storing means for storing a plurality of transformation affine matrices Mwo which transform a world coordinate system of the three-dimensional space to the shape prescription coordinate systems prescribing the shapes of the objects stored in the shape storing means;

    Mow matrix storing means for storing a plurality of transformation affine matrices Mow which transform the shape prescription coordinate systems prescribing the shapes of the objects stored in the shape storing means to the world coordinate system;

    input means for inputting a piece of movement data designating an amount of a parallel translation, a rotational motion and an isotropic magnification or minification of the first object;

    movement matrix generating means for generating movement matrices indicating the parallel translation, the rotational motion and the isotropic magnification or minification of the first object according to the movement data input to the input means;

    affine matrix calculating means for calculating a transformation affine matrix Mow(new) relating to the first object moved or transformed according to the movement data by utilizing the movement matrices generated in the movement matrix generating means and a transformation affine matrix Mow which relates to the first object not moved nor transformed and is stored in the Mow matrix storing means, the transformation affine matrix Mow(new) being stored in the Mow matrix storing means to replace the transformation affine matrix Mow with the transformation affine matrix Mow(new);

    an inverse matrix calculating apparatus for calculating an inverse matrix Mow-1 (new) of the transformation affine matrix Mow(new) stored in the Mow matrix storing means, the inverse matrix calculating apparatus comprisingaffine matrix dividing means for dividing the transformation affine matrix Mow(new) into a minor matrix Q indicating the rotational motion and the isotropic magnification or minification of the first object and a position vector p indicating the parallel translation of the first object,transposed matrix calculating means for calculating a transposed matrix Qt of the minor matrix Q divided in the affine matrix dividing means,vector-matrix multiplying means for multiplying the position vector p divided in the affine matrix dividing means by the transposed matrix Qt calculated in the transposed matrix calculating means to produce a vector pQt and changing a sign of the matrix pQt to produce a multiplied vector -pQt,inner product calculating means for calculating a squared product of an absolute value of an axial vector composing the minor matrix Q as a squared rate of the isotropic magnification or minification,dividing means for dividing each of components of the transposed matrix Qt calculated in the transposed matrix calculating means and each of components of the multiplied vector -pQt obtained in the vector-matrix multiplying means by the squared product calculated in the inner product calculating means, andinverse affine matrix arranging means for arranging the transposed matrix Qt divided by the squared product in the dividing means as a minor matrix of the inverse matrix Mow-1 (new) and arranging the multiplied vector -pQt divided by the squared product in the dividing means as a position vector of the inverse matrix Mow-1 (new) to produce the inverse matrix Mow-1 (new) having the minor matrix Qt divided by the squared product and the position vector -pQt divided by the squared product, the inverse matrix Mow-1 (new) being stored in the Mwo matrix storing means as a transformation affine matrix Mwo(new) relating to the first object moved or transformed to replace a transformation affine matrix Mwo which is stored in the Mwo matrix storing means and relates to the first object not moved nor transformed with the inverse matrix Mow-1 (new);

    inter-object processing means for transforming the shape prescription coordinate systems prescribing the shapes of the first and second objects stored in the shape storing means to the world coordinate system according to a transformation affine matrix Mow of the second object and the transformation affine matrix Mow(new) of the first object stored in the Mow matrix storing means, changing the shapes of the first and second objects prescribed in the world coordinate system to processed shapes while incorporating an inter-object relationship between the first and second objects in the processed shapes, transforming the world coordinate system prescribing the processed shapes of the first and second objects to the shape prescription coordinate systems of the first and second objects according to a transformation affine matrix Mwo of the second object and the transformation affine matrix Mwo(new) of the first object stored in the Mwo matrix storing means, and replacing the shapes of the first and second objects stored in the shape storing means with the processed shapes of the first and second objects prescribed in the shape prescription coordinate systems; and

    displaying means for displaying the processed shapes of the first and second objects stored in the shape storing means.

View all claims
  • 1 Assignment
Timeline View
Assignment View
    ×
    ×