Curved surface designing method

• US 5,185,855 A
• Filed: 10/07/1991
• Issued: 02/09/1993
• Est. Priority Date: 07/29/1987
• Status: Expired due to Fees

• Current Assignee: Mitsubishi Denki Kabushiki Kaisha (Mitsubishi Electric Corporation)
• Original Assignee: Mitsubishi Denki Kabushiki Kaisha (Mitsubishi Electric Corporation)
• Inventors: Kato, Kiyotaka, Okamoto, Takashi
• Primary Examiner(s): Harkcom, Gary V.
• Assistant Examiner(s): Nguyen, Phu K.
• Application Number:
  US07/770,787
• Time in Patent Office: 491 Days
• Field of Search: 340/728, 340/747, 340/701, 340/703, 395/128, 395/129, 395/141, 395/142, 395/143, 364/468, 364/474.24
• US Class Current: 345/441
• CPC Class Codes: G05B 19/4099 Surface or curve machining, making 3D objects, e.g. desktop manufacturing
• CPC Class Codes: G05B 19/41 characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path G05B19/25, G05B19/31, G05B19/37, G05B19/39, G05B19/40 take precedence
• CPC Class Codes: G06T 17/20 Finite element generation, e.g. wire-frame surface description, tesselation
• CPC Class Codes: Y02P 90/02 Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Abstract

A curved surface designing method comprises the steps of a first step of inputting edge shape data of n-sides of a curved surface, a second step of obtaining a regular n-sided polygon in a parameter space on the basis of the given data of n sides, a third step of calculating distance parameters on the basis of the regular n-sided polygon obtained by the second step, a fourth step of calculating blending values on the basis of the distance parameters, a fifth step of mapping an inner point D of the regular n-sided polygon onto the respective sides so as to calculate boundary parameters, a sixth step of calculating at least one of three-dimensional coordinate points, and, if necessary, tangent vectors, on sides which are boundaries of the curved surface on the basis of the boundary parameters, and a seventh step of calculating arbitrary points on the curved surface on the basis of the distance parameters, the blending values, the three-dimensional coordinate points of the respective sides, and, if necessary, the tangent vectors, of the respective sides.

Claims

1. A method of operating a CAD/CAM system comprising designing a curved surface in accordance with input data and generating control signals for said CAD/CAM system in accordance with the designed curved surface, said method comprising the steps of:

a first step of inputting data identifying a number n of sides of a polygonal curved surface as well as edge shape data for said sides, where n is an integer greater than 3;

a second step of generating a regular n-sided polygon in a two-dimensional parameter space in accordance with the number n of the inputted sides;

a third step of obtaining perpendiculars from an arbitrary point P inside said regular n-sided polygon onto the sides thereof or prolonged lines of said sides in said two-dimensional parameter space in accordance with the number n of the inputted sides;

a fourth step of obtaining the length of said perpendiculars between said point P and respective sides of said polygon as distance parameters;

a fifth step of obtaining blending values which take the value 1 on one of said sides of said n-sided polygon and the value 0 on the other sides, which blending values are interpolated smoothly from the value 0 to the value 1 within said regular n-sides polygon, a partial differential of each blending value with respect to one of said distance parameters having a value of zero at the side associated with said one distance parameter;

a sixth step of mapping said point P onto said sides and obtaining, as boundary parameters, ratios of the portions of said sides which are divided by said mapped points;

a seventh step of generating three-dimensional coordinate values and values of tangent vectors on said sides on the basis of said boundary parameters;

an eighth step of calculating points on said curved surface on the basis of said distance parameters, said blending values, said three-dimensional coordinate values and said tangent vectors; and

a ninth step of generating said control signals for controlling said CAD/CAM system, using said calculated points.

2. A curved surface designing method according to claim 1, wherein said first step further comprises a step of inputting tangent vectors on said sides.

3. A curved surface designing method according to claim 1, wherein the boundary parameter for each side is a ratio between distance parameters of the sides adjacent to said each side.

4. A curved surface designing method according to claim 1, wherein the boundary parameter for each side is a rate at which a point R on said each side divides said each side, said point R being defined as an intersecting point between said each side and a straight line connecting said point P and a point of intersection between prolonged lines of the two sides adjacent to said each side.

5. A curved surface designing method according to claim 1, wherein said three-dimensional coordinate values and the values of said tangent vectors are expressed by control points bearing a predetermined positional relationship to each side.

6. A curved surface designing method according to claim 1, said method further comprising the steps of:

a ninth step of producing a tool locus in said two-dimensional parameter space; and

a tenth step of calculating a locus on said curved surface on the basis of said tool locus and calculating a real three-dimensional tool locus on the basis of said locus.

7. A curved surface designing method according to claim 6, wherein said first step further comprises a step of inputting tangent vectors on said sides.

8. A curved surface designing method according to claim 6, wherein the boundary parameter for each side is a ratio between distance parameters of the sides adjacent to said each side.

9. A curved surface designing method according to claim 6, wherein the boundary parameter for each side is a rate at which a point R on said each side divides said each side, said point R being defined as an intersecting point between said each side and a straight line connecting said point P and a point of intersection between prolonged lines of the two sides adjacent to said each side.

10. A curved surface designing method according to claim 6, wherein said three-dimensional coordinate values and the values of said tangent vectors are expressed by control points bearing a predetermined positional relationship to each side.

11. A curved surface designing method according to claim 1, said method further comprising the steps of:

a ninth step of drawing and displaying the obtained curved surface on a display; and

a tenth step of producing a tool locus in said two-dimensional parameter space.

12. A curved surface designing method according to claim 11, wherein said first step further comprises a step of inputting tangent vectors on said sides.

13. A curved surface designing method according to claim 11, wherein the boundary parameter for each side is a ratio between distance parameters of the sides adjacent to said each side.

14. A curved surface designing method according to claim 11, wherein the boundary parameter for each side is a rate at which a point R on said each side divides said each side, said point R being defined as an intersecting point between said each side and a straight line connecting said point P and a point of intersection between prolonged lines of the two sides adjacent to said each side.

15. A curved surface designing method according to claim 11, wherein said three-dimensional coordinate values and the values of said tangent vectors are expressed by control points bearing a predetermined positional relationship to each side.

16. The method of claim 1 further comprising using said control signals to control the machining of a work piece with a numerical control (NC) machine tool.

17. A method of operating a machining device for machining a workpiece, said method comprising the steps of designing a curved surface in accordance with data input via an input device, providing machining control output data in accordance with the designed surface, and controlling said machining device to operate on said workpiece in accordance with the machining control output data, said method comprising the steps of:

a first step of inputting data identifying a number n of sides of a polygonal curved surface as well as edge shape data for said sides, where n is an integer greater than 3;

a second step of generating a regular n-sided polygon in a two-dimensional parameter space in accordance with the number n of the inputted sides;

a third step of obtaining perpendiculars from an arbitrary point P inside said regular n-sided polygon onto the sides thereof or prolonged lines of said sides in said two-dimensional parameter space in accordance with the number n of the inputted sides;

a fourth step of obtaining the length of said perpendiculars between said point P and respective sides of said polygon as distance parameters;

a fifth step of obtaining blending values which take the value 1 on one of said sides of said n-sided polygon and the value 0 on the other sides, which blending values are interpolated smoothly from the value 0 to the value 1 within said regular n-sided polygon, a partial differential of each blending value with respect to one of said distance parameters having a value of zero at the side associated with said one distance parameter;

a sixth step of mapping said point P onto said sides and obtaining, as boundary parameters, ratios of the portions of said sides which are divided by said mapped points;

a seventh step of generating three-dimensional coordinate values and values of tangent vectors on said sides on the basis of said boundary parameters;

an eighth step of calculating points on said curved surface on the basis of said distance parameters, said blending values, said three-dimensional coordinate values and said tangent vectors;

a ninth step of generating said machining control output data in accordance with said calculated points; and

a tenth step of controlling said machining device in accordance with said machining control output data.

18. A method of fabricating an article via a machining system, said method comprising the steps of inputting data via a data input device, processing said data in a data processing device to design at least one curved surface of said article, and driving a machine tool in accordance with the results of said processing to machine a workpiece to form said article, wherein:

said step of inputting data comprises

inputting data identifying a number n of sides of a polygonal curved surface as well as edge shape data for said sides, where n is an integer greater than 3;

said step of processing said data comprises

generating a regular n-sided polygon in a two-dimensional parameter space in accordance with the number n of the inputted sides;

obtaining perpendiculars from an arbitrary point P inside said regular n-sided polygon onto the sides thereof or prolonged lines of said sides in said two-dimensional parameter space in accordance with the number n of the inputted sides;

obtaining the length of said perpendiculars between said point P and respective sides of said polygon as distance parameters;

obtaining blending value which take the value 1 on one of said sides of said n-sided polygon and the value 0 on the other sides, which blending values are interpolated smoothly from the value 0 to the value 1 within said regular n-sided polygon, a partial differential of each blending value with respect to one of said distance parameters having a value of zero at the side associated with said one distance parameter;

mapping said point P onto said sides and obtaining, as boundary parameters, ratios of the portions of said sides which are divided by said mapped points;

generating three-dimensional coordinate values and values of tangent vectors on said sides on the basis of said boundary parameters; and

calculating points on said curved surface on the basis of said distance parameters, said blending values, said three-dimensional coordinate values and said tangent vectors; and

said step of driving said machine tool comprises

generating control signals in accordance with said calculated points; and

driving said machine tool in accordance with said control signals.