Engraving a 2D image on a subdivision surface

1. A computer-implemented method for designing a 3D modeled object, the method comprising:

defining, by a user, a base mesh associated to a subdivision surface and to a corresponding predetermined mesh-to-NURBS-surface conversion algorithm PCCM(⋅), the subdivision surface representing the 3D modeled object;

defining, by the user, a 2D image and a location for engraving the 2D image on the subdivision surface; and

determining a non-uniform rational basis spline (NURBS) surface S 1 that corresponds to applying a deformation map i,j Δ(i,j) on the result S 0 =PCCM(B 0 ) of performing the mesh-to-NURBS-surface conversion algorithm to the base mesh, the deformation map including displacement vectors provided for positions of the result of performing the mesh-to-NURBS-surface conversion algorithm to the base mesh, the positions corresponding to the location for engraving the 2D image, the displacement vectors being computed based on corresponding pixel values of the 2D image,

wherein the corresponding pixel values of the 2D image are pixel grayscale values, and

wherein the NURBS surface is determined based on magnitudes of the pixel grayscale values.

2. The method of claim 1 , wherein the method comprises computing the displacement vectors, including:

determining, from the base mesh, a first 3D mesh that corresponds to the location for engraving the 2D image;

determining, from the first 3D mesh, a second 3D mesh B 5 (i)=B 4 (i)+d i N(i) by displacing vertices of the first 3D mesh, in a direction normal to the first 3D mesh, based on the corresponding pixel values of the 2D image; and

computing, for positions of the result of performing the mesh-to-NURBS-surface conversion algorithm to the base mesh, a displacement vector Δ(i,j)=c i,j (S 5 )−C i,j (S 4 ) equal to the 3D position difference between the corresponding control point (C i,j (S 5 )) of the result S 5 =PCCM(B 5 ) of performing the mesh-to-NURBS-surface conversion algorithm to the second 3D mesh and the corresponding control point (C i,j (S 4 ) of the result S 4 =PCCM(B 4 ) of performing the mesh-to-NURBS-surface conversion algorithm to the first 3D mesh.

3. The method of claim 2 , wherein determining the first 3D mesh includes extracting a sub-mesh of the base mesh that corresponds to the location for engraving the 2D image, and then subdividing the sub-mesh a predetermined number of times.

4. The method of claim 3 , wherein the predetermined number of times is defined by the user and/or increasingly depends on a predetermined criterion associated to a level of details of the 2D image.

5. The method of claim 1 , wherein the amplitude of a displacement vector increasingly depends on the corresponding grayscale value.

6. The method of claim 1 , wherein the user further selects an engraving direction from a predetermined binary list.

7. A non-transitory computer readable medium storing a computer file including specifications of:

a base mesh associated to a subdivision surface and to a corresponding predetermined mesh-to-NURBS-surface conversion algorithm, the subdivision surface representing the 3D modeled object; and

a 2D image and a location for engraving the 2D image on the subdivision surface,

wherein the computer file being implemented by processing circuitry to

define, by a user, a base mesh associated to a subdivision surface and to a corresponding predetermined mesh-to-NURBS-surface conversion algorithm, the subdivision surface representing the 3D modeled object;

define, by the user, a 2D image and a location for engraving the 2D image on the subdivision surface; and

determine a non-uniform rational basis spline (NURBS) surface that corresponds to applying a deformation map on the result of performing the mesh-to-NURBS-surface conversion algorithm to the base mesh, the deformation map including displacement vectors provided for positions of the result of performing the mesh-to-NURBS-surface conversion algorithm to the base mesh, the positions corresponding to the location for engraving the 2D image, the displacement vectors being computed based on corresponding pixel values of the 2D image,

wherein the corresponding pixel values of the 2D image are pixel grayscale values, and

wherein the NURBS surface is determined based on magnitudes of the pixel grayscale values.

8. A non-transitory data storage medium having recorded thereon a computer program comprising instructions for performing a method for designing a 3D modeled object, the method comprising:

defining, by a user, a base mesh associated to a subdivision surface and to a corresponding predetermined mesh-to-NURBS-surface conversion algorithm, the subdivision surface representing the 3D modeled object;

defining, by the user, a 2D image and a location for engraving the 2D image on the subdivision surface; and

determining a non-uniform rational basis spline (NURBS) surface that corresponds to applying a deformation map on the result of performing the mesh-to-NURBS-surface conversion algorithm to the base mesh, the deformation map including displacement vectors provided for positions of the result of performing the mesh-to-NURBS-surface conversion algorithm to the base mesh, the positions corresponding to the location for engraving the 2D image, the displacement vectors being computed based on corresponding pixel values of the 2D image,

wherein the corresponding pixel values of the 2D image are pixel grayscale values, and

wherein the NURBS surface is determined based on magnitudes of the pixel grayscale values.

9. A CAD system comprising a processor coupled to a GUI and to a non-transitory memory, the non-transitory memory having recorded thereon a computer program comprising instructions for performing a method for designing a 3D modeled object, the method comprising:

defining, by a user, a base mesh associated to a subdivision surface and to a corresponding predetermined mesh-to-NURBS-surface conversion algorithm, the subdivision surface representing the 3D modeled object;

defining, by the user, a 2D image and a location for engraving the 2D image on the subdivision surface; and

determining a non-uniform rational basis spline (NURBS) surface that corresponds to applying a deformation map on the result of performing the mesh-to-NURBS-surface conversion algorithm to the base mesh, the deformation map including displacement vectors provided for positions of the result of performing the mesh-to-NURBS-surface conversion algorithm to the base mesh, the positions corresponding to the location for engraving the 2D image, the displacement vectors being computed based on corresponding pixel values of the 2D image,

wherein the corresponding pixel values of the 2D image are pixel grayscale values, and

wherein the NURBS surface is determined based on magnitudes of the pixel grayscale values.