Method and apparatus for generating a topologically consistent visual representation of a three dimensional surface

Claim 1

A method for producing a visual representation of a three dimensional body, the method comprising: providing a computer having a memory; generating a three dimensional signal pattern that represents the values of a physical property associated with a three dimensional body at spaced apart locations within the body; generating a threshold value of the physical property, the threshold value and the three dimensional signal pattern defining a three dimensional isosurface that partitions the three dimensional signal pattern into pattern groupings; converting the three dimensional signal pattern into a set of data vectors, each data vector having a physical property component and a location component corresponding to a respective one of the spaced apart locations; storing the data vectors in the memory of the computer using the computer to sort the data vectors, so as to create a first and second group of data vectors, the first group including data vectors having a physical property component less than the threshold value, the second group including data vectors having a physical property component greater than the threshold value; using the computer to generate coordinates of a set of polygon vertex points approximately lying on the three dimensional isosurface, coordinates of each member of the set of polygon vertex points being interpolated using a respective data vector belonging to the first group and a respective data vector belonging to the second group; using the computer to generate a body saddle value from data vectors having location components that are spatially coadjacent with one another; using the computer to compare the threshold value to the body saddle value; linking two members of the set of polygon vertex points if the body saddle value and values associated with the two members are all greater than the threshold value; linking two members of the set of polygon vertex points if the body saddle value and values associated with the two members are all less than the threshold value; using the linked members of the set of polygon vertex points to generate a piecewise polygonal approximation that is topologically consistent with the isosurface, in that the polygonal approximation partitions the signal pattern into the same pattern groupings as does the isosurface; and using the polygonal approximation to generate an image representative of the body.

Claim 2

A method for producing a visual representation of a three dimensional body, the method comprising: providing a computer having a memory; generating a three dimensional signal pattern that represents the values of a physical property associated with a three dimensional body at spaced apart locations within the body; generating a threshold value of the physical property, the threshold value and the three dimensional signal pattern defining a three dimensional isosurface that partitions the three dimensional signal pattern into pattern groupings; converting the three dimensional signal pattern into a set of data vectors, each data vector having a physical property component and a location component corresponding to a respective one of the spaced apart locations; storing the data vectors in the memory of the computer using the computer to sort the data vectors, so as to create a first and second group of data vectors, the first group including data vectors having a physical property component less than the threshold value, the second group including data vectors having a physical property component greater than the threshold value; using the computer to generate coordinates of a set of polygon vertex points approximately lying on the three dimensional isosurface, coordinates of each member of the set of polygon vertex points being interpolated using a respective data vector belonging to the first group and a respective data vector belonging to the second group; using the computer to generate a body saddle value from data vectors having location components that are spatially coadjacent with one another; using the computer to compare the threshold value to the body saddle value; linking two members of the set of polygon vertex points if the body saddle value and values associated with the two members are all greater than the threshold value; linking two members of the set of polygon vertex points if the body saddle value and values associated with the two members are all less than the threshold value; using the linked members of the set of polygon vertex points to generate a piecewise polygonal approximation that is topologically consistent with the isosurface, in that the polygonal approximation partitions the signal pattern into the same pattern groupings as does the isosurface; and using the polygonal approximation to generate an image representative of the body.

Claim 14

An apparatus for producing a visual representation of a three dimensional isosurface, comprising: a computer having a memory measurement means for generating a three dimensional signal pattern that represents the values of a physical property associated with a three dimensional body at spaced apart locations within said body; input means for generating a threshold value of the physical property, the threshold value and the three dimensional signal pattern defining a three dimensional isosurface that partitions the three dimensional signal pattern into pattern groupings; means for converting the three dimensional signal pattern into a set of data vectors, each data vector having a physical property component and a location component corresponding to a respective one of the spaced apart locations; means for storing the data vectors in the memory of the computer means for sorting the data vectors, so as to create a first and second group of data vectors, the first group including data vectors having a physical property component less than the threshold value, the second group including data vectors having a physical property component greater than the threshold value; means for generating coordinates of a set of polygon vertex points approximately lying on the three dimensional isosurface, coordinates of each member of the set of polygon vertex points being interpolated using a respective data vector belonging to the first group and a respective data vector belonging to the second group; means for generating a body saddle value from data vectors having location components that are spatially coadjacent with one another; means for comparing the threshold value to the body saddle value; means for linking two members of the set of polygon vertex points if the body saddle value and values associated with the two members are all greater than the threshold value; means for linking two members of the set of polygon vertex points if the body saddle value and values associated with the two members are all less than the threshold value means for linking members of the set of polygon vertex points to generate a piecewise polygonal approximation that is topologically consistent with the isosurface, in that the polygonal approximation partitions the signal pattern into the same pattern groupings as does the isosurface; and display means coupled with the computer for using the polygonal approximation to generate an image representative of the body.

Claim 15

An apparatus for producing a visual representation of a three dimensional isosurface, comprising: a computer having a memory measurement means for generating a three dimensional signal pattern that represents the values of a physical property associated with a three dimensional body at spaced apart locations within said body; input means for generating a threshold value of the physical property, the threshold value and the three dimensional signal pattern defining a three dimensional isosurface that partitions the three dimensional signal pattern into pattern groupings; means for converting the three dimensional signal pattern into a set of data vectors, each data vector having a physical property component and a location component corresponding to a respective one of the spaced apart locations; means for storing the data vectors in the memory of the computer means for sorting the data vectors, so as to create a first and second group of data vectors, the first group including data vectors having a physical property component less than the threshold value, the second group including data vectors having a physical property component greater than the threshold value; means for generating coordinates of a set of polygon vertex points approximately lying on the three dimensional isosurface, coordinates of each member of the set of polygon vertex points being interpolated using a respective data vector belonging to the first group and a respective data vector belonging to the second group; means for generating a body saddle value from data vectors having location components that are spatially coadjacent with one another; means for comparing the threshold value to the body saddle value; means for linking two members of the set of polygon vertex points if the body saddle value and values associated with the two members are all greater than the threshold value; means for linking two members of the set of polygon vertex points if the body saddle value and values associated with the two members are all less than the threshold value means for linking members of the set of polygon vertex points to generate a piecewise polygonal approximation that is topologically consistent with the isosurface, in that the polygonal approximation partitions the signal pattern into the same pattern groupings as does the isosurface; and display means coupled with the computer for using the polygonal approximation to generate an image representative of the body.