Abstract: A method and system provide the ability to design a surface. An existing triangular surface mesh representative of an existing surface is obtained. A modification to the mesh in compliance with design constraints is received. A volume level set or a volume minimization set, for the modified mesh, is obtained in Euclidean space. A volume subgradient set based on the volume level set, is obtained. A scalar is determined and used to scale heights between vertices of a triangle. A projection is computed and may be scaled. The projection may then be removed from the triangle's vertices. The removing changes the triangular surface mesh into a converged triangular surface mesh that minimizes an objective function. The objective function computes an absolute earthwork volume and/or an absolute value of a net volume representing the difference between a fill and cut of earthwork material.

Abstract: A method and system provide the ability to design a (land) surface. A triangular surface mesh representative of an existing surface is obtained. The mesh includes triangles that are connected by vertices and edges. Design constraint sets are determined based design constraints. The design constraints include a maximum slope constraint for a first triangle of the two or more triangles in the triangular surface mesh. The maximum slope constraint is a maximum angle between a normal vector of the first triangle and a reference vector. Heights of the vertices of the first triangle are projected onto the design constraint sets such that the normal vector satisfies all of the design constraints. The projecting includes modifying the heights by a minimum Euclidian distance. A design of the surface represented by the triangular surface mesh is generated based on the projecting.

Abstract: A method and system provide the ability to design a surface. An existing triangular surface mesh representative of an existing surface is obtained. A modification to the mesh in compliance with design constraints is received. A volume level set or a volume minimization set, for the modified mesh, is obtained in Euclidean space. A volume subgradient set based on the volume level set, is obtained. A scalar is determined and used to scale heights between vertices of a triangle. A projection is computed and may be scaled. The projection may then be removed from the triangle's vertices. The removing changes the triangular surface mesh into a converged triangular surface mesh that minimizes an objective function. The objective function computes an absolute earthwork volume and/or an absolute value of a net volume representing the difference between a fill and cut of earthwork material.

Abstract: A method and system provide the ability to design a (land) surface. A triangular surface mesh representative of an existing surface is obtained. The mesh includes triangles that are connected by vertices and edges. Design constraint sets are determined based design constraints. The design constraints include a maximum slope constraint for a first triangle of the two or more triangles in the triangular surface mesh. The maximum slope constraint is a maximum angle between a normal vector of the first triangle and a reference vector. Heights of the vertices of the first triangle are projected onto the design constraint sets such that the normal vector satisfies all of the design constraints. The projecting includes modifying the heights by a minimum Euclidian distance. A design of the surface represented by the triangular surface mesh is generated based on the projecting.