Dividing cubes and method for the display of surface structures contained within the interior region of a solid body

Claim 1

A system for displaying three dimensional surface structures, said system comprising: means for storing three-dimensional signal patterns representing the value of at least one physical property associated with a three dimensional body at regularly spaced parallelopiped grid locations defining volume elements within said body; means for retrieving the thirty-two three dimensional signal pattern values associated with each set of eight cubically adjacent grid locations and the twenty-four additional grid locations adjacent to said eight cubically adjacent grid locations, each of said cubically adjacent grid locations being associated with three of said additional grid locations; first comparison means for comparing the signal values associated with said eight adjacent grid locations with a predetermined threshhold value to determine those volume elements for which at least one of said eight comparison results is distinct from the other seven comparison results so as to identify selected volume elements through which a surface determined by said threshhold value passes; first generating means for generating normal vectors from said thirty-two signal pattern values for each of said eight cubically adjacent grid locations associated with each selected volume element; second generating means for generating, for each selected volume element defined by said eight cubically adjacent grid locations, a plurality of additional signal values associates with additional spacial locations defined along the edges and within the interior of said selected volume element, said additional spacial locations corresponding to subdivision of said volume element; - second comparison means for comparing the signal values associated with each set of eight cubically adjacent spacial locations associated with each of said volume element subdivisions with said predetermined threshhold value to determine those subdivided volume elements for which at least one of said subdivision comparison results is distinct from the other seven comparison results, so as to generate a sequence of values identifying selected grid and additional spacial locations which at least approximately lie on a surface determined by said threshhold value; third generating means for generating normal vectors associated with said additional spacial locations, said selected grid locations and additionally selected spacial locations being generated so as to be associated with the corresponding normal vectors for said locations; and display processor means for receiving said associated location values and normal vectors and providing a shaded image on a screen, said image representing said surface determined by said threshhold. 2. A method for displaying three dimensional surface structures, said system comprising: storing three-dimensional signal patterns representing the value of at least one physical property associated with a three dimensional body at regularly spaced parallelopiped grid locations defining volume elements within said body; retrieving the thirty-two three dimensional signal pattern values associated with each set of eight cubically adjacent grid locations and the twenty-four additional grid locations adjacent to said eight cubically adjacent grid locations, each of said cubically adjacent grid locations being associated with three of said additional grid locations; comparing the signal values associated with said eight adjacent grid locations with a predetermined threshhold value to determine those volume elements for which at least one of said eight comparison results is distinct from the other seven comparison results so as to identify selected volume elements through which a surface determined by said threshhold value passes; generating normal vectors from said thirty-two signal pattern values for each of said eight cubically adjacent grid locations associated with each selected volume element; generating, for each selected volume element defined by said eight cubically adjacent grid locations, a plurality of additional signal values associates with additional spacial locations defined along the edges and within the interior of said selected volume element, said additional spacial locations corresponding to subdivision of said volume element; comparing the signal values associated with each set of eight cubically adjacent spacial locations associated with each of said volume element subdivisions with said predetermined threshhold value to determine those subdivided volume elements for which at least one of said subdivision comparison results is distinct from the other seven comparison results, so as to generate a sequence of values identifying selected grid and additional spacial locations which at least approximately lie on a surface determined by said threshhold value; generating normal vectors associated with said additional spacial locations, said selected grid locations and additionally selected spacial locations being generated so as to be associated with the corresponding normal vectors for said locations; and receiving said associated location values and normal vectors in a display processor operating to provide a shaded image on a screen, said image representing said surface determined by said threshhold.

Claim 2

A system for displaying three dimensional surface structures, said system comprising: means for storing three-dimensional signal patterns representing the value of at least one physical property associated with a three dimensional body at regularly spaced parallelopiped grid locations defining volume elements within said body; means for retrieving the thirty-two three dimensional signal pattern values associated with each set of eight cubically adjacent grid locations and the twenty-four additional grid locations adjacent to said eight cubically adjacent grid locations, each of said cubically adjacent grid locations being associated with three of said additional grid locations; first comparison means for comparing the signal values associated with said eight adjacent grid locations with a predetermined threshhold value to determine those volume elements for which at least one of said eight comparison results is distinct from the other seven comparison results so as to identify selected volume elements through which a surface determined by said threshhold value passes; first generating means for generating normal vectors from said thirty-two signal pattern values for each of said eight cubically adjacent grid locations associated with each selected volume element; second generating means for generating, for each selected volume element defined by said eight cubically adjacent grid locations, a plurality of additional signal values associates with additional spacial locations defined along the edges and within the interior of said selected volume element, said additional spacial locations corresponding to subdivision of said volume element; - second comparison means for comparing the signal values associated with each set of eight cubically adjacent spacial locations associated with each of said volume element subdivisions with said predetermined threshhold value to determine those subdivided volume elements for which at least one of said subdivision comparison results is distinct from the other seven comparison results, so as to generate a sequence of values identifying selected grid and additional spacial locations which at least approximately lie on a surface determined by said threshhold value; third generating means for generating normal vectors associated with said additional spacial locations, said selected grid locations and additionally selected spacial locations being generated so as to be associated with the corresponding normal vectors for said locations; and display processor means for receiving said associated location values and normal vectors and providing a shaded image on a screen, said image representing said surface determined by said threshhold. 2. A method for displaying three dimensional surface structures, said system comprising: storing three-dimensional signal patterns representing the value of at least one physical property associated with a three dimensional body at regularly spaced parallelopiped grid locations defining volume elements within said body; retrieving the thirty-two three dimensional signal pattern values associated with each set of eight cubically adjacent grid locations and the twenty-four additional grid locations adjacent to said eight cubically adjacent grid locations, each of said cubically adjacent grid locations being associated with three of said additional grid locations; comparing the signal values associated with said eight adjacent grid locations with a predetermined threshhold value to determine those volume elements for which at least one of said eight comparison results is distinct from the other seven comparison results so as to identify selected volume elements through which a surface determined by said threshhold value passes; generating normal vectors from said thirty-two signal pattern values for each of said eight cubically adjacent grid locations associated with each selected volume element; generating, for each selected volume element defined by said eight cubically adjacent grid locations, a plurality of additional signal values associates with additional spacial locations defined along the edges and within the interior of said selected volume element, said additional spacial locations corresponding to subdivision of said volume element; comparing the signal values associated with each set of eight cubically adjacent spacial locations associated with each of said volume element subdivisions with said predetermined threshhold value to determine those subdivided volume elements for which at least one of said subdivision comparison results is distinct from the other seven comparison results, so as to generate a sequence of values identifying selected grid and additional spacial locations which at least approximately lie on a surface determined by said threshhold value; generating normal vectors associated with said additional spacial locations, said selected grid locations and additionally selected spacial locations being generated so as to be associated with the corresponding normal vectors for said locations; and receiving said associated location values and normal vectors in a display processor operating to provide a shaded image on a screen, said image representing said surface determined by said threshhold.