Fitting sample points with an isovalue surface

Patent metadata

Field	Value
Publication number	US-9928314-B2
Application number	US-201514684147-A
Country	US
Kind code	B2
Filing date	Apr 10, 2015
Priority date	Apr 10, 2014
Publication date	Mar 27, 2018
Grant date	Mar 27, 2018

Abstract

The invention notably relates to a computer-implemented method for designing a three-dimensional modeled object that represents a physical entity. The method comprises providing sample points; determining a volumetric function, within a predetermined class of volumetric functions, as the optimum of an optimization program that explores orientation vectors defined at the sample points, wherein the optimization program penalizes a distance from the explored orientation vectors; and fitting the sample points with an isovalue surface of the volumetric function, wherein the program further penalizes oscillations of the fitted isovalue surface.

First claim

The invention claimed is:

1. A computer-implemented method for generating a three-dimensional modeled object that represents a physical entity, comprising:
providing sample points;
determining a volumetric function, within a predetermined class of volumetric functions, as the optimum of an optimization program that explores orientation vectors defined at the sample points, wherein the optimization program penalizes a distance from the explored orientation vectors, wherein the distance from the explored orientation vectors involves a difference between a gradient of an argument volumetric function and an explored orientation vector at the sample points;
fitting the sample points with an isovalue surface of the volumetric function, wherein the optimization program further penalizes oscillations of the isovalue surface; and
displaying the three-dimensional modeled object generated based on the fitting.

2. The method of claim 1 , wherein the oscillations for an explored volumetric function involve a volume integral of a positive function of a derivation of the explored volumetric function.

3. The method of claim 2 , wherein the positive function is a square function.

4. The method of claim 2 , wherein the derivation of the explored volumetric function is a normalization of the explored volumetric function obtained by subtracting an average value of the volumetric function at the sample points.

5. The method of claim 4 , wherein the optimization program is: F

F
*

⁡

(
p
)

=

f
⁡

(

argmax

θ
,
ϕ

⁢

∫

∫
∫

V

⁢

f
⁡

(

θ
,
ϕ
,
p

)

nor
2

⁢
d
⁢

⁢
ν

,
p

)

where:
p={p 1 . . . p N } are the sample points,
F is the predetermined class of volumetric functions, defined on volume domain V, and

f
⁡

(

θ
,
ϕ
,
p

)

nor

=

f
⁡

(

θ
,
ϕ
,
p

)

-

∑
i

⁢

f

θ
,
ϕ

⁡

(

p
i

)

N

is the normalization of the explored volumetric function ƒ(θ, φ, p)=argmin ƒϵF Σ i ∥∇ƒ(p i )−n θ i φ i ∥, wherein N={n θ i φ i . . . n θ N φ N } are explored orientation vectors defined at the sample points P by azimuth and elevation angles θ={θ 1 . . . θ N } and φ={φ 1 . . . φ N }.

6. The method of claim 1 , wherein the sample points correspond to 3D curves sketched by a user and the optimization program explores the orientation vectors under a constraint that the explored orientation vectors be normal to the 3D curves and respect a minimal rotation propagation condition over each 3D curve.

7. The method of claim 6 , wherein the constraint that the explored orientation vectors respect the minimal rotation propagation condition corresponds to an application of a double reflection method.

8. The method of claim 6 , wherein the determining comprises solving the optimization program by a meta-heuristic optimization.

9. The method of claim 8 , wherein the meta-heuristic optimization is a particle swarm optimization.

10. The method of claim 9 , wherein the distance from the explored orientation vectors involves a sum of norms of the difference between the gradient of the argument volumetric function and the explored orientation vector at the sample points.

11. The method of claim 1 , wherein the physical entity is a manufacturing product.

12. A non-transitory data storage medium having recorded thereon a computer program that comprises instructions for performing a method of generating a three-dimensional modeled object that represents a physical entity, wherein the method comprises:
providing sample points;
determining a volumetric function, within a predetermined class of volumetric functions, as the optimum of an optimization program that explores orientation vectors defined at the sample points, wherein the optimization program penalizes a distance from the explored orientation vectors, wherein the distance from the explored orientation vectors involves a difference between a gradient of an argument volumetric function and an explored orientation vector at the sample points;
fitting the sample points with an isovalue surface of the volumetric function, wherein the computer program further penalizes oscillations of the isovalue surface; and
displaying the three-dimensional modeled object generated based on the fitting.

13. A system comprising a processor coupled to a memory and a graphical user interface, the memory having rec

Assignees

• Dassault Systemes

Inventors

• Bonner David Leo

Classifications

• G06T17/00 Primary

  Three-dimensional [3D] modelling for computer graphics · CPC title

• G06F17/175 Primary

  of multidimensional data · CPC title

• G06F30/17

  Mechanical parametric or variational design · CPC title

• G06F17/10

  Complex mathematical operations {(function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544)} · CPC title

• G06T2210/56

  Particle system, point based geometry or rendering · CPC title