Abstract
In computer graphics and geometric modeling, polyhedron's inside test, a determination whether a given point lies inside or outside a polyhedron, plays an important role. However, this cannot be realized easily. Since former methods have some difficulties, a yew method of design is introduced in this papaer.
When all polygons of polyhedron's faces are projected ont.o a sphere whose center lies on the given point with radius of 1, the sum of area becomes 4π i f the point lies inside the polyhedron. Otherwise, this becomes 0. Though it is difficult to calculate an area of the polygon on the sphere, it can be calculated by dividing the polygon into triangles.
This new algorithm of inside test was programmed and applied to two kinds of object, one, a cube and the other an octagonal prism. As a result, the errors of area's calculation for 4π was under 0.03%. These figures confirms that the test can be applied to rather complex objects.
