SYSTEM, METHOD, AND COMPUTER PROGRAM PRODUCT FOR ANGULAR SUBDIVISION OF QUADRATIC BEZIER CURVES

• US 20150178961A1
• Filed: 12/20/2013
• Published: 06/25/2015
• Est. Priority Date: 12/20/2013
• Status: Abandoned Application

• Current Assignee: NVIDIA Corporation
• Original Assignee: NVIDIA Corporation
• Inventors: Karras, Tero Tapani
• Application Number:
  US14/137,881
• Publication Number:
  US 20150178961A1
• Time in Patent Office: Days
• US Class Current: 1/1
• CPC Class Codes: G06F 17/175 of multidimensional data
• CPC Class Codes: G06T 11/203 Drawing of straight lines or curves

Abstract

A system, method, and computer program product are provided for subdividing a quadratic Bezier curve. The method includes the steps of receiving a quadratic Bezier curve defined by a plurality of control points including at least a first endpoint and a second endpoint. The quadratic Bezier curve is uniformly subdivided based on an angle between a first tangent at the first endpoint and a second tangent at the second endpoint to produce a piecewise representation of the quadratic Bezier curve including two or more Bezier curve segments.

Claims

1. A method comprising:

receiving a Bezier curve defined by a plurality of control points including at least a first endpoint and a second endpoint; and

subdividing, by a processor, the Bezier curve uniformly based on an angle between a first tangent at the first endpoint and a second tangent at the second endpoint to produce a piecewise representation of the Bezier curve including two or more Bezier curve segments.

2. The method of claim 1, wherein the Bezier curve is a quadratic Bezier curve that defines a portion of a two-dimensional path and the two or more Bezier curve segments are quadratic Bezier curves.

3. The method of claim 2, further comprising, prior to receiving the Bezier curve, approximating the two-dimensional path to produce a set of quadratic Bezier curves including the quadratic Bezier curve.

4. The method of claim 1, further comprising determining a pair of approximate offset curves corresponding to the two or more Bezier curve segments based on a stroke width parameter.

5. The method of claim 4, further comprising filling a region between the pair of approximate offset curves to stroke a portion of the two-dimensional path that is represented by the two or more Bezier curve segments.

6. The method of claim 1, further comprising, prior to subdividing, determining a number of Bezier curve segments into which the Bezier curve is subdivided.

7. The method of claim 6, wherein the number is computed based on the angle and a predetermined error value.

8. The method of claim 7, wherein the predetermined error value is based on a curve offset parameter.

9. The method of claim 1, wherein each Bezier curve segment is defined by a first segment endpoint and a second segment endpoint, and the angles between a first segment tangent at the first segment endpoint and a second segment tangent at the second segment endpoint for each Bezier curve segment are equal.

10. The method of claim 9, wherein the first and the second relative angles equal the angle divided by a quantity of the two or more Bezier curve segments into which the Bezier curve is subdivided.

11. The method of claim 1, wherein each processing thread in a set of processing threads is assigned to calculate one Bezier curve segment of the Bezier curve segments.

12. A system comprising:

a memory configured to store a Bezier curve defined by a plurality of control points including at least a first endpoint and a second endpoint; and

a processor that is configured to;

receive the Bezier curve; and

subdivide the Bezier curve uniformly based on an angle between a first tangent at the first endpoint and a second tangent at the second endpoint to produce a piecewise representation of the Bezier curve including two or more Bezier curve segments.

13. The system of claim 12, wherein the Bezier curve is a quadratic Bezier curve that defines a portion of a two-dimensional path and the two or more Bezier curve segments are quadratic Bezier curves.

14. The system of claim 13, wherein the processor is further configured to, prior to receiving the Bezier curve, approximate the two-dimensional path to produce a set of quadratic Bezier curves including the quadratic Bezier curve.

15. The system of claim 12, wherein the processor is further configured to determine a pair of approximate offset curves corresponding to the two or more quadratic Bezier curve segments based on a stroke width parameter.

16. The system of claim 15, wherein the processor is further configured to fill a region between the pair of approximate offset curves to stroke a portion of the two-dimensional path that is represented by the two or more Bezier curve segments.

17. The system of claim 12, wherein the processor is further configured to, prior to subdividing, determine a number of Bezier curve segments into which the Bezier curve is subdivided.

18. The system of claim 17, wherein the number is computed based on the angle and a predetermined error value.

19. The system of claim 12, wherein each Bezier curve segment is defined by a first segment endpoint and a second segment endpoint, and the angles between a first segment tangent at the first segment endpoint and a second segment tangent at the second segment endpoint for each Bezier curve segment are equal.

20. A computer-readable storage medium storing instructions that, when executed by a processor, causes the processor to perform steps comprising:

receiving a Bezier curve defined by a plurality of control points including at least a first endpoint and a second endpoint; and

subdividing, by a processor, the Bezier curve uniformly based on an angle between a first tangent at the first endpoint and a second tangent at the second endpoint to produce a piecewise representation of the Bezier curve including two or more Bezier curve segments.