Method for modeling and rendering complex surfaces using local height maps

A method of rendering, comprising:

• specifying a three-dimensional surface to be rendered by specifying a plurality of footpoints and a plurality of corresponding surface heights, the surface height being of a surface point corresponding to the footpoint, the footpoint being in a polygon used to approximate the surface;
• computing display properties for a pixel in an image of the surface by finding a first point of collision of a first ray with the surface through the pixel in a viewing direction;
• and
• finding a second point of collision of a second ray with the surface usinig a Lipshitz constant.

A computer readable medium containing instructions which, when executed in a processing system, causes the processing systems to perform a method for modeling a three-dimensional surface, comprising:

• approximating a three-dimensional surface with a polygonal mesh, each polygon of the polygonal mesh containing a plurality of footpoints;
• associating a normal vector with each vertex of the polygon;
• interpolating a normal vector at each footpoint from the vertex normals of the polygon containing the footpoint;
• and
• associating a height with each point on the three-dimensional surface in a neighborhood of the corresponding polygon, the height representing a signed distance from a footpoint along the corresponding interpolated normal vector to the point on the three-dimensional surface.

A computer readable medium containing instructions which, when executed in a processing system, causes the processing systems to perform a method for rendering a three-dimensional surface, comprising:

• specifying a three-dimensional surface to be rendered by specifying a plurality of footpoints and a plurality of corresponding surface heights, the surface height being of a surface point corresponding to the footpoint, the footpoint being in a polygon used to approximate the surface;
• computing display properties for a pixel in an image of the surface by finding a first point of collision with the surface of a first ray through the pixel in a viewing direction;
• and
• finding a second point of collision of a second ray with the surface using a Lipshitz constant.

An apparatus, comprising:

• means for approximating a three-dimensional surface with a polygonal mesh, each polygon of the polygonal mesh containing a plurality of footpoints;
• means for associating a normal vector with each vertex of the polygon;
• means for interpolating a normal vector at each footpoint from the vertex normals of the polygon containing the footpoint;
• and
• means for associating a height with each point on the three-dimensional surface in a neighborhood of the corresponding polygon, the height representing a signed distance from a footpoint along the corresponding interpolated normal vector to the point on the three-dimensional surface.