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US 8,818,771 B2Granted
Computer implemented tool box systems and methods
OwnerJohan Gielis, Diego Caratelliinventors
Life of this patent
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Abstract
According to the preferred embodiments, a system or method is provided that involves the programming of a computer or other processing device with a software, hardware or firmware configured to create a processing tool (i.e., referred to herein as a tool box) that can be configured to provide one or more operational function based on new mathematical principles described herein for the purposes of, e.g., synthesizing or analyzing shapes and the like.
Claims13
A method of optimizing a shape of a product, comprising:
- a) providing a computer programmed to solve the following equation related to differential problems in a two dimensional domain whose boundary is described by a general k-type Gielis curve
-
- ρ
- =
- R
-
- (
- ϑ
- )
- =
- ∑
- j
- =
- 0
- k
-
- r
- G
-
- (
- ϑ
- ;
- γ
- j
-
- (
- ϑ
- )
- ,
- m
- j
- ,
- a
- j
- ,
- b
- j
- ,
- n
- 1
-
- j
- ,
- n
- 2
-
- j
- ,
- n
- 3
-
- j
- )
- ,
-
- where
-
-
-
- r
- G
-
- (
- ϑ
- ;
- γ
-
- (
- ϑ
- )
- ,
- a
- ,
- b
- ,
- m
- ,
- n
- 1
- ,
- n
- 2
- ,
- n
- 3
- )
- =
- γ
-
- (
- ϑ
- )
- ·
- [
-
- 1
- a
- ·
- cos
-
-
- m
- 4
-
- ϑ
-
- n
- 2
- +
-
- 1
- b
- ·
- sin
-
-
- m
- 4
-
- ϑ
-
- n
- 3
- ]
- -
- 1
- /
- n
- 1
- denotes an ordinary Gielis polar equation modulated by a smooth function γ(θ), wherein a, b, n1, n2, n3 and m are finite real numbers, and n1, a and b≠0,
- b) storing a data set depicting an environment related to the product,
- c) using the computer to determine an optimal shape in relation to said data set with said equation, and
- d) constructing the product with an optimal shape based on said optimal shape determined in said step c).
130 more elements
A system for optimizing a shape of a product, comprising:
- a) a computer programmed to solve the following equation related to differential problems in a two dimensional domain whose boundary is described by a general k-type Gielis curve
-
- ρ
- =
- R
-
- (
- ϑ
- )
- =
- ∑
- j
- =
- 0
- k
-
- r
- G
-
- (
- ϑ
- ;
- γ
- j
-
- (
- ϑ
- )
- ,
- m
- j
- ,
- a
- j
- ,
- b
- j
- ,
- n
- 1
-
- j
- ,
- n
- 2
-
- j
- ,
- n
- 3
-
- j
- )
- ,
-
- where
-
-
-
- r
- G
-
- (
- ϑ
- ;
- γ
-
- (
- ϑ
- )
- ,
- a
- ,
- b
- ,
- m
- ,
- n
- 1
- ,
- n
- 2
- ,
- n
- 3
- )
- =
- γ
-
- (
- ϑ
- )
- ·
- [
-
- 1
- a
- ·
- cos
-
-
- m
- 4
-
- ϑ
-
- n
- 2
- +
-
- 1
- b
- ·
- sin
-
-
- m
- 4
-
- ϑ
-
- n
- 3
- ]
- -
- 1
- /
- n
- 1
- denotes an ordinary Gielis polar equation modulated by a smooth function γ(θ), wherein a, b, n1, n2, n3 and m are finite real numbers, and n1, a and b≠0,
- b) a database storing a data set depicting an environment related to the product,
- c) said computer being configured determine an optimal shape in relation to said data set using said equation.
129 more elements
Dependencies are inferred from the claim text.