Method for Efficiently Computing and Specifying Level Sets for Use in Computer Simulations, Computer Graphics and Other Purposes

Abstract

Surface features might represent features of a virtual fluid and a method might include obtaining a digital representation of the virtual fluid defined at least in part by an implicit surface, obtaining a digital representation of a collection of points defined relative to the implicit surface whereat the surface features are to be determined. A point of the collection of points might have associated therewith a plurality of attribute values specifying a property of the surface features. For an input point, a corresponding implicit surface point might be determined, along with, for the corresponding implicit surface point, a subset of the points within a search region. Interpolated attribute values might be obtained from attribute values associated with points of the subset, and a surface displacement value computed from interpolated attribute values. A dataset corresponding to the surface features might be generated.

1 - 15 . (canceled) 
     
     
         16 . A computer-implemented method for sampling surface features of a virtual fluid positioned in a virtual space, the virtual fluid defined, at least in part, by an implicit surface, the computer-implemented method comprising:
 obtaining a first digital representation of the virtual fluid;   obtaining a second digital representation of a collection of points in the virtual space wherein, for at least some points of the collection of points, points at which surface features are to be determined are defined in the second digital representation relative to at least a portion of the implicit surface;   determining a plurality of attribute values specifying a property of the surface features for the points;   determining, for an input point of the collection of points, a corresponding implicit surface point;   determining a search region relative to the corresponding implicit surface point;   determining a subset of the collection of points within the search region; and   generating a dataset corresponding to the surface features based, at least on, the subset of the collection of points within the search region.   
     
     
         17 . The computer-implemented method of  claim 16 , further comprising:
 determining a set of interpolated attribute values associated with points of the subset of the collection of points;   computing a computed surface displacement value from the set of interpolated attribute values; and   wherein generating the dataset is further based on the computed surface displacement value.   
     
     
         18 . The computer-implemented method of  claim 17 , wherein determining the set of interpolated attribute values comprises interpolating attributes of the set of interpolated attribute values. 
     
     
         19 . The computer-implemented method of  claim 16 , wherein the property of the surface features is a displacement from the implicit surface. 
     
     
         20 . The computer-implemented method of  claim 16 , wherein determining the corresponding implicit surface point for the input point comprises:
 determining a first signed distance field value for the input point;   determining a first field gradient value for the input point; and   determining the corresponding implicit surface point from a position of the input point, the first signed distance field value, and the first field gradient value.   
     
     
         21 . The computer-implemented method of  claim 16 , wherein the first digital representation represents the virtual fluid in a Eulerian grid representation and the second digital representation represents a mesh region as a plurality of Lagrangian points. 
     
     
         22 . The computer-implemented method of  claim 16 , wherein one or more visual representations of the surface features depict capillary waves on a surface of the virtual fluid. 
     
     
         23 . The computer-implemented method of  claim 16 , wherein the collection of points is defined at a higher resolution than the implicit surface. 
     
     
         24 . The computer-implemented method of  claim 16 , wherein the plurality of attribute values comprises a phase value and/or an amplitude value. 
     
     
         25 . The computer-implemented method of  claim 16 , wherein determining the subset of the collection of points within the search region comprises:
 using ray casting to cast a ray from the input point through the corresponding implicit surface point;   identifying one or more intersected polygons of a plurality of polygons that are intersected by the ray;   determining a plurality of vertices corresponding to vertices of one or more polygon of the one or more intersected polygons; and   processing the plurality of vertices as the subset of the collection of points.   
     
     
         26 . The computer-implemented method of  claim 25 , wherein the ray extends from the input point passing through the corresponding implicit surface point to a ray endpoint that is a predetermined distance from the corresponding implicit surface point along the ray. 
     
     
         27 . The computer-implemented method of  claim 25 , wherein the ray extends to a sample position for which a signed distance between the sample position and the implicit surface meets a maximum-displacement threshold. 
     
     
         28 . The computer-implemented method of  claim 27 , further comprising:
 obtaining a second plurality of distances for a second plurality of sample positions, wherein the second plurality of sample positions includes a particular sample position for which the signed distance between the particular sample position and the implicit surface does not meet the maximum-displacement threshold, each distance of the second plurality of distances being equal to the signed distance between the particular sample position and the implicit surface; and   generating one or more visual representations is based on at least some of the second plurality of distances.   
     
     
         29 . A computer system for generating one or more visual representations of surface features of a virtual fluid, the computer system comprising:
 at least one processor; and   a computer-readable medium storing instructions, which when executed by the at least one processor, causes the computer system to carry out the method of claim  1 .   
     
     
         30 . A non-transitory computer-readable storage medium storing instructions, which when executed by at least one processor of a computer system, causes the computer system to carry out the method of claim  1 . 
     
     
         31 . A computer system for generating one or more visual representations of surface features of a virtual fluid positioned in a virtual space, the virtual fluid defined, at least in part, by an implicit surface, the computer system comprising:
 a first storage for a first digital representation of the virtual fluid;   a second storage for a second digital representation of a collection of points in the virtual space wherein, for at least some points of the collection of points, points at which surface features are to be determined are defined in the second digital representation relative to at least a portion of the implicit surface;   a processor for:
 a) determining determined points of the collection of points at which of the surface features are defined in the second digital representation relative to at least the portion of the implicit surface; 
 b) determining a plurality of attribute values specifying a property of the surface features for the determined points; 
 c) determining, for an input point of the collection of points, a corresponding implicit surface point; 
 d) determining a search region relative to the corresponding implicit surface point; 
 e) determining a subset of the collection of points within the search region; and 
 f) generating a dataset corresponding to the surface features based, at least on, the subset of the collection of points within the search region. 
   
     
     
         32 . The computer system of  claim 31 , wherein the first digital representation represents the virtual fluid in a Eulerian grid representation and the second digital representation represents a mesh region as a plurality of Lagrangian points. 
     
     
         33 . The computer system of  claim 31 , wherein the one or more visual representations depict capillary waves on a surface of the virtual fluid. 
     
     
         34 . The computer system of  claim 31 , wherein the property of the surface features is a displacement from the implicit surface and wherein the plurality of attribute values comprises a phase value and/or an amplitude value.