A method generating a display of a surface, and an apparatus for carrying out such a method

摘要

In order to generate a display of a surface, an equation or equations are generated corresponding to all or parts of the surface ( GAMMA ). The equation or equations represent the surface as a physical membrane. Boundary conditions ( DIFFERENTIAL GAMMA ) of the surface ( GAMMA ) can thus be specified, and the equation solved, using the boundary conditions ( DIFFERENTIAL GAMMA ) as outer constraints, to generate a display of the surface. A set of points (C, D, E) within the boundary of the surface ( GAMMA ) may be specified, which then define inner constraints for the solution of the equation. Where parts ( GAMMA <1>, GAMMA <2>, GAMMA <3>) of the surface join at a point (P123) or line ( DIFFERENTIAL gamma <1><2>) , a further equation can be generated, which further equation represents the area ( GAMMA <1><2>, GAMMA <1><2><3>) around the join as a physical membrane. Solution of that equation, preserving the boundary of the area ( GAMMA <1><2>, GAMMA <1><2><3>) around the join, provides a smooth transition between the parts ( GAMMA <1>, GAMMA <2>, GAMMA <3>) of the surface.