Abstract: A computer-implemented method converts a raw drawing into an artist-intended curve drawing. The method comprises: obtaining a raw drawing comprising a plurality of strokes; clustering the plurality of strokes into one or more clusters, each cluster comprising a corresponding group of strokes; for each more cluster, performing a curve fitting to determine a computer representation of a corresponding aggregate curve that is fitted to the group of strokes in the cluster; and generating a computer representation of an artist-intended curve drawing corresponding to the raw drawing. The curve drawing comprises the aggregate curve in place of the group of strokes corresponding to each cluster. Clustering the plurality of strokes into one more clusters comprises performing a plurality of iterative procedures to either group strokes into precursor clusters or to divide precursor clusters into precursor sub-clusters based on human perception models.

Abstract: A method is for estimating a three-dimensional (3D) representation of a set of two-dimensional (2D) curves of a concept drawing, the estimate of the 3D representation corresponding to a 3D object underlying the concept drawing. The method comprises: obtaining a representation of a set of 2D curves a concept drawing that represent a 3D object underlying the concept drawing; determining an energy function based on the set of 2D curves, the energy function comprising one or more terms, each term reflective of a preference for a 3D representation based on a characteristic of the 2D curves which reflects how concept drawings are commonly perceived to represent 3D objects; and performing an optimization which minimizes the energy function to thereby determine the 3D representation.

Abstract: Methods and systems improve quality of a hex-mesh by: performing a first iterative procedure which starts with the input hex-mesh and which outputs an output hex-mesh having improved quality. Performing the first iterative procedure comprises: initializing a current hex-mesh to be equal to the input hex mesh; for each iteration of the first iterative procedure: performing an optimization of an energy function over a plurality of directed-edges in the current hex-mesh to determine updated vertex positions for vertices in the current hex-mesh, wherein for each directed edge, the energy function comprises a term that expresses a preference for the directed edge to be aligned with normal vectors of base triangles of an edge-cone corresponding to the directed edge; and updating the current hex-mesh with the updated vertex positions; and after one or more iterations, setting the output hex-mesh to be equal to the current hex-mesh.

Abstract: A method for generating a polycube representation of an input object comprises: receiving an input volumetric representation of the input object; deforming the input volumetric representation to provide a deformed object representation; and extracting, by the processor, a polycube representation of the object from the deformed object representation. Deforming the input volumetric representation to provide the deformed object representation comprises effecting a tradeoff between competing objectives of: deforming the input volumetric representation in a manner which provides surfaces having normal vectors closely aligned with one of the six directions aligned with the set of global Cartesian axes; and deforming the input volumetric representation in a manner which provides low-distortion deformations. Deforming the input volumetric representation to provide the deformed object may be performed iteratively.

Abstract: Methods for characterizing two-dimensional concept drawings are disclosed. The concept drawings comprise cross-sections intersecting at cross-hairs. The method comprises: determining, for each cross-section: a plane on which the cross-section is located, the plane having a normal vector in a three-dimensional coordinate system; and, for each cross-hair on the cross-section, a tangent vector in the three-dimensional coordinate system which is tangent to the cross-section at the cross-hair. For each cross-hair comprising ith and jth intersecting cross-sections, one or more constraints are satisfied, the constraints comprising: the normal vector ni of the plane on which the ith cross-section is located is at least approximately orthogonal to the normal vector nj of the plane on which the jth cross-section is located; and the tangent vector tij to the ith cross-section at the cross-hair is at least approximately orthogonal to the tangent vector tji to the jth cross-section at the cross-hair.

Abstract: A method for generating a polycube segmentation of an input object comprises: providing an input mesh of the object comprising a plurality of surface faces; generating an initial polycube labeling for the faces by assigning, to each face, a label which is one of six directions (±X,±Y,±Z) aligned with a set of Cartesian axes, the initial polycube labeling defining a plurality of charts, and generating the initial polycube labeling comprising effecting a tradeoff between competing objectives of: making the initial polycube labeling relatively compact; and making the initial polycube labeling relatively faithful to the input object. The method further comprises generating an updated polycube segmentation by changing the label assigned to each of one or more surface faces and thereby modifying one or more of the charts to provide the charts with monotonic boundaries.

Abstract: A method for generating a polycube representation of an input object comprises: receiving an input volumetric representation of the input object; deforming the input volumetric representation to provide a deformed object representation; and extracting, by the processor, a polycube representation of the object from the deformed object representation. Deforming the input volumetric representation to provide the deformed object representation comprises effecting a tradeoff between competing objectives of: deforming the input volumetric representation in a manner which provides surfaces having normal vectors closely aligned with one of the six directions aligned with the set of global Cartesian axes; and deforming the input volumetric representation in a manner which provides low-distortion deformations. Deforming the input volumetric representation to provide the deformed object may be performed iteratively.

Abstract: A method is for estimating a three-dimensional (3D) representation of a set of two-dimensional (2D) curves of a concept drawing, the estimate of the 3D representation corresponding to a 3D object underlying the concept drawing. The method comprises: obtaining a representation of a set of 2D curves a concept drawing that represent a 3D object underlying the concept drawing; determining an energy function based on the set of 2D curves, the energy function comprising one or more terms, each term reflective of a preference for a 3D representation based on a characteristic of the 2D curves which reflects how concept drawings are commonly perceived to represent 3D objects; and performing an optimization which minimizes the energy function to thereby determine the 3D representation.

Abstract: Methods and systems improve quality of a hex-mesh by: performing a first iterative procedure which starts with the input hex-mesh and which outputs an output hex-mesh having improved quality. Performing the first iterative procedure comprises: initializing a current hex-mesh to be equal to the input hex mesh; for each iteration of the first iterative procedure: performing an optimization of an energy function over a plurality of directed-edges in the current hex-mesh to determine updated vertex positions for vertices in the current hex-mesh, wherein for each directed edge, the energy function comprises a term that expresses a preference for the directed edge to be aligned with normal vectors of base triangles of an edge-cone corresponding to the directed edge; and updating the current hex-mesh with the updated vertex positions; and after one or more iterations, setting the output hex-mesh to be equal to the current hex-mesh.

Abstract: Methods for characterizing two-dimensional concept drawings are disclosed. The concept drawings comprise cross-sections intersecting at cross-hairs. The method comprises: determining, for each cross-section: a plane on which the cross-section is located, the plane having a normal vector in a three-dimensional coordinate system; and, for each cross-hair on the cross-section, a tangent vector in the three-dimensional coordinate system which is tangent to the cross-section at the cross-hair. For each cross-hair comprising ith and jth intersecting cross-sections, one or more constraints are satisfied, the constraints comprising: the normal vector ni of the plane on which the ith cross-section is located is at least approximately orthogonal to the normal vector nj of the plane on which the jth cross-section is located; and the tangent vector tij to the ith cross-section at the cross-hair is at least approximately orthogonal to the tangent vector tji to the jth cross-section at the cross-hair.

Abstract: A method for generating a polycube segmentation of an input object comprises: providing an input mesh of the object comprising a plurality of surface faces; generating an initial polycube labeling for the faces by assigning, to each face, a label which is one of six directions (±X,±Y,±Z) aligned with a set of Cartesian axes, the initial polycube labeling defining a plurality of charts, and generating the initial polycube labeling comprising effecting a tradeoff between competing objectives of: making the initial polycube labeling relatively compact; and making the initial polycube labeling relatively faithful to the input object. The method further comprises generating an updated polycube segmentation by changing the label assigned to each of one or more surface faces and thereby modifying one or more of the charts to provide the charts with monotonic boundaries.

Abstract: Methods for characterizing two-dimensional concept drawings are disclosed. The concept drawings comprise cross-sections intersecting at cross-hairs. The method comprises: determining, for each cross-section: a plane on which the cross-section is located, the plane having a normal vector in a three-dimensional coordinate system; and, for each cross-hair on the cross-section, a tangent vector in the three-dimensional coordinate system which is tangent to the cross-section at the cross-hair. For each cross-hair comprising ith and jth intersecting cross-sections, one or more constraints are satisfied, the constraints comprising: the normal vector ni of the plane on which the ith cross-section is located is at least approximately orthogonal to the normal vector nj of the plane on which the jth cross-section is located; and the tangent vector tij to the ith cross-section at the cross-hair is at least approximately orthogonal to the tangent vector tji to the jth cross-section at the cross-hair.

Abstract: Processing method for transforming a first surface into a second surface, according to which: a/ in a (k+1)th iteration step, for each couple comprising a first elementary surface and a second elementary surface transformed from the first elementary surface in iteration k, the projection of the second elementary surface on the plane of the first elementary surface is determined and a matrix (A) is defined for said couple, where (A)=pkt,(pt)?1 and pt=[pn+1?pi]i=1 to n, pkt,=[p?n+1,k?p?i,k]i=1 to n; b/ the second elementary surfaces obtained for the (k+1)th iteration are determined as those minimizing a function including at least the term Eshape—k+1=(B).

Abstract: Processing method for transforming a first surface into a second surface, according to which: a/ in a (k+1)th iteration step, for each couple comprising a first elementary surface and a second elementary surface transformed from the first elementary surface in iteration k, the projection of the second elementary surface on the plane of the first elementary surface is determined and a matrix (A) is defined for said couple, where (A)=Pkt,(Pt)?1 and Pt=[pn+1?pi]i=1 to n, Pkt,=[p?n+1,k?p?i,k]i=1 to n; b/ the second elementary surfaces obtained for the (k+1)th iteration are determined as those minimizing a function including at least the term Eshape—k+1=(B).

Abstract: Methods for characterizing two-dimensional concept drawings are disclosed. The concept drawings comprise cross-sections intersecting at cross-hairs. The method comprises: determining, for each cross-section: a plane on which the cross-section is located, the plane having a normal vector in a three-dimensional coordinate system; and, for each cross-hair on the cross-section, a tangent vector in the three-dimensional coordinate system which is tangent to the cross-section at the cross-hair. For each cross-hair comprising ith and jth intersecting cross-sections, one or more constraints are satisfied, the constraints comprising: the normal vector ni of the plane on which the ith cross-section is located is at least approximately orthogonal to the normal vector nj of the plane on which the jth cross-section is located; and the tangent vector tij to the ith cross-section at the cross-hair is at least approximately orthogonal to the tangent vector tji to the jth cross-section at the cross-hair.

Abstract: A method for generating a polycube representation of an input object comprises: receiving an input volumetric representation of the input object; deforming the input volumetric representation to provide a deformed object representation; and extracting, by the processor, a polycube representation of the object from the deformed object representation. Deforming the input volumetric representation to provide the deformed object representation comprises effecting a tradeoff between competing objectives of: deforming the input volumetric representation in a manner which provides surfaces having normal vectors closely aligned with one of the six directions aligned with the set of global Cartesian axes; and deforming the input volumetric representation in a manner which provides low-distortion deformations. Deforming the input volumetric representation to provide the deformed object may be performed iteratively.