Method and system for minimizing earthwork volumes

A computer-implemented method for designing a surface, comprising:

• (a) obtaining, in a computer, an existing triangular surface mesh representative of an existing surface, wherein the existing triangular surface mesh comprises a first triangle and one or more additional triangles connected by vertices and edges;
• (b) receiving a modification to the first triangle in compliance with one or more design constraints, resulting in a modified first triangle;
• (c) obtaining a net volume minimization set, in Euclidean space, for the modified first triangle;
• (d) determining a projection, of one or more heights of the vertices of the modified first triangle onto the net volume minimization set, wherein the projection comprises a direction and a distance;
• (f) determining a scalar to reduce the distance;
• (g) applying the scalar to reduce the distance of the projection, wherein:
• (i) the applying changes the existing triangular surface mesh into a converged triangular surface mesh;
• (ii) the converged triangular surface mesh minimizes one or more objective functions;
• (iii) one or more of the objective functions computes an absolute value of one or more net volumes;
• (iv) each net volume of the one or more net volumes comprises a difference between a fill and a cut of earthwork material resulting from modifying the existing triangular surface mesh into the converged triangular surface mesh.

A computer-implemented system for designing a surface, comprising:

• (a) a computer having a memory;
• (b) a processor executing on the computer;
• (c) the memory storing a set of instructions, wherein the set of instructions, when executed by the processor cause the processor to perform operations comprising:
• (1) obtaining, in a computer, an existing triangular surface mesh representative of an existing surface, wherein the existing triangular surface mesh comprises a first triangle and one or more additional triangles connected by vertices and edges;
• (2) receiving a modification to the first triangle in compliance with one or more design constraints, resulting in a modified first triangle;
• (3) obtaining a volume level set, in Euclidean space, for the modified first triangle;
• (4) obtaining a volume subgradient set based on the volume level set, in the Euclidean space;
• (5) determining a scalar from the area of the first triangle or the modified first triangle;
• (6) scaling heights between the vertices of the modified first triangle and the first triangle using the scalar;
• (7) computing a projection, of one or more scaled heights of the vertices of the modified first triangle onto the volume subgradient set;
• (8) scaling the projection using the scalar;
• (9) removing the scaled projection from the vertices of the modified first triangle, wherein:
• (i) the removing changes the triangular surface mesh into a converged triangular surface mesh;
• (ii) the converged triangular surface mesh minimizes one or more objective functions;
• (iii) one or more of the objective functions computes an absolute earthwork volume between the first triangle on the existing surface and the modified first triangle on the converged triangular surface mesh.

A computer-implemented system for designing a surface, comprising:

• (a) a computer having a memory;
• (b) a processor executing on the computer;
• (c) the memory storing a set of instructions, wherein the set of instructions, when executed by the processor cause the processor to perform operations comprising:
• (1) obtaining, in a computer, an existing triangular surface mesh representative of an existing surface, wherein the existing triangular surface mesh comprises a first triangle and one or more additional triangles connected by vertices and edges;
• (2) receiving a modification to the first triangle in compliance with one or more design constraints, resulting in a modified first triangle;
• (3) obtaining a net volume minimization set, in Euclidean space, for the modified first triangle;
• (4) determining a projection, of one or more heights of the vertices of the modified first triangle onto the net volume minimization set, wherein the projection comprises a direction and a distance;
• (5) determining a scalar to reduce the distance;
• (6) applying the scalar to reduce the distance of the projection, wherein:
• (i) the applying changes the existing triangular surface mesh into a converged triangular surface mesh;
• (ii) the converged triangular surface mesh minimizes one or more objective functions;
• (iii) one or more of the objective functions computes an absolute value of one or more net volumes;
• (iv) each net volume of the one or more net volumes comprises a difference between a fill and a cut of earthwork material resulting from modifying the existing triangular surface mesh into the converged triangular surface mesh.