Interpolating sample values from known triangle vertex values

• US 20020050979A1
• Filed: 08/24/2001
• Published: 05/02/2002
• Est. Priority Date: 08/24/2000
• Status: Active Grant

• Current Assignee: Oracle America, Inc. (Oracle Corporation)
• Original Assignee: Sun Microsystems Incorporated (Oracle Corporation)
• Inventors: Arcuri, Salvatore, Deering, Michael F., Oberoi, Ranjit S.
• Granted Patent: US 6,747,663 B2
• Time in Patent Office: Days
• US Class Current: 345/157
• CPC Class Codes: G06T 15/80 Shading

Abstract

A graphics system comprises a rendering unit, a sample buffer and a sample-to-pixel calculation unit. The rendering unit receives graphics data specifying three triangle vertices, generates sample positions, and determines which samples reside inside the triangle. The rendering unit computes an axial rate of change of an ordinate based on the positions and ordinates of the vertices, and, for each sample residing inside the triangle, (a) multiplies the axial rate by a edge-relative sample displacement resulting in a first product, (b) interpolates a projection value for a projection point on a first edge of the triangle, and (c) adds the first product to the projection value resulting in a sample ordinate value. The sample buffer stores the sample ordinate value the samples inside the triangle. The sample-to-pixel calculation unit reads sample ordinate values from the sample buffer and generates a pixel value by filtering the sample ordinate values

Claims

1. A rendering unit comprising:

sample position generation logic configured to generate sample positions in a two-dimensional screen space;

sample testing logic configured to receive graphics data including three vertices defining a triangle and to determine which of said sample positions reside inside the triangle;

sample ordinate generation logic coupled to the sample position generation logic and the sample testing logic, wherein the sample ordinate generation logic is configured to compute a first axial rate of change of a first ordinate based on the three vertices, and, for each sample position residing inside the triangle, (a) to multiply the first axial rate by a first sample displacement resulting in a first product, (b) to interpolate a first projection value for a projection point on a first edge of the triangle, and (c) to add the first product to the first projection value resulting in a first sample ordinate value, wherein the first sample ordinate value is usable to determine at least a portion of a displayable image.

2. The rendering unit of claim 1, wherein the sample testing logic is further configured to compute a horizontal edge displacement and a vertical edge displacement for each of the triangle edges, to determine a major displacement as the maximum of the horizontal edge displacement and a vertical edge displacement for each edge, to determine the first edge as the edge whose major displacement is greater than or equal to the major displacements for all other edges of the triangle.

3. The rendering unit of claim 1, wherein the sample ordinate generation logic is further configured to compute the first axial rate by:

determining a change in the first ordinate between an opposing vertex not on the first edge and an auxiliary point on the first edge having an identical first axis coordinate as the opposing vertex, determining a coordinate change along the first axis between the opposing vertex and the auxiliary point, and multiplying the first ordinate change by the reciprocal of the first axis coordinate change.

4. The rendering unit of claim 3, wherein the sample ordinate generation logic is configured to determine the first ordinate change by interpolating an auxiliary ordinate value for the auxiliary point based on a first vertex and a second vertex terminating the first edge and, subtracting the auxiliary ordinate value from an opposing ordinate value of the opposing vertex.

5. The rendering unit of claim 1, wherein the sample ordinate generation logic is configured to interpolate the first projection value for the projection point by computing a first difference between a first coordinate of the projection point and a first coordinate of a first vertex of the first edge, multiplying the first difference by a first scaling factor resulting in a second difference, and adding the second difference to a root ordinate value corresponding to the first vertex.

6. The rendering unit of claim 5, wherein the sample ordinate generation logic is configured to compute the first scaling factor by determining an ordinate change between a second vertex of the first edge and the first vertex, determining a second difference between a first coordinate of the second vertex and the first coordinate of the first vertex, and multiplying the ordinate change by the reciprocal of the second difference.

7. The rendering unit of claim 1, wherein the sample testing logic is configured to determine if each sample position resides inside the triangle by computing edge-relative displacements between the sample position and the three edges of the triangle, wherein the first sample displacement comprises the edge-relative displacement for the first edge.

8. The rendering unit of claim 1, wherein the first ordinate is selected from the group consisting of red, green, blue, transparency, texture, depth, magenta, cyan, yellow, gray-scale.

9. The rendering unit of claim 1, wherein the sample position logic is configured to generate the sample positions according to a perturbed regular sample-positioning scheme or a stochastic sample positioning scheme.

10. The rendering unit of claim 1, wherein the sample ordinate generation logic comprises dedicated hardware to compute the first axial rate, and to perform (a), (b), (c) for each sample position inside the triangle.

11. The rendering unit of claim 1 further comprising:

a sample buffer configured to store the first sample ordinate value for each of the sample positions inside the triangle; and

a sample-to-pixel calculation unit configured to read one or more of the first sample ordinate values from the sample buffer, to generate a pixel value by filtering the one or more first sample ordinate values, and to supply the pixel value to a display device.

14. The method of claim 13 further comprising:

computing a horizontal edge displacement and a vertical edge displacement for each of the triangle edges;

determining a major displacement as the maximum of the horizontal edge displacement and a vertical edge displacement for each edge;

determining the first edge as the edge whose major displacement is greater than or equal to the major displacements for all other edges of the triangle.

15. The method of claim 13, wherein said computing the first axial rate comprises:

determining a change in the first ordinate between an opposing vertex not on the first edge and an auxiliary point on the first edge having an identical first axis coordinate as the opposing vertex;

determining a coordinate change along the first axis between the opposing vertex and the auxiliary point; and

multiplying the first ordinate change by the reciprocal of the first axis coordinate change.

16. The method of claim 15, wherein said determining the first ordinate change comprises:

interpolating an auxiliary ordinate value for the auxiliary point based on a first vertex and a second vertex terminating the first edge; and

subtracting the auxiliary ordinate value from an opposing ordinate value of the opposing vertex.

17. The method of claim 13, wherein said interpolating the first projection value for the projection point comprises:

computing a first difference between a first coordinate of the projection point and a first coordinate of a first vertex of the first edge;

multiplying the first difference by a first scaling factor resulting in a second difference; and

adding the second difference to a root ordinate value corresponding to the first vertex.

18. The method of claim 17, wherein said computing the first scaling factor comprises:

determining an ordinate change between a second vertex of the first edge and the first vertex;

determining a second difference between a first coordinate of the second vertex and the first coordinate of the first vertex; and

multiplying the ordinate change by the reciprocal of the second difference.

19. The method of claim 13 further comprising determining if each of said sample positions reside inside the triangle by computing edge-relative displacements between the sample positions and the three edges of the triangle, wherein the first sample displacement comprises the edge-relative displacement for the first edge.

20. The method of claim 13, wherein the first ordinate is selected from the group consisting of red, green, blue, transparency, texture, depth, magenta, cyan, yellow, gray-scale.

21. The method of claim 13 further comprising:

operating on the first sample ordinate values corresponding to one or more sample positions to generate a pixel value; and

transmitting the pixel value to a display device.

12. A graphics system comprising:

an input configured to receive graphics data including three vertices defining a triangle; and

a rendering unit coupled to the input and configured to receive the graphics data including the three vertices defining the triangle from the input unit, wherein the rendering unit is further configured to generate samples in a two-dimensional screen space, wherein the rendering unit is configured to determine which of said samples reside inside the triangle;

wherein said rendering unit is configured to compute a first axial rate of change of a first ordinate based on the three vertices, and, for each sample residing inside the triangle, (a) to multiply the first axial rate by a first sample displacement resulting in a first product, (b) to interpolate a first projection value for a projection point on a first edge of the triangle, and (c) to add the first product to the first projection value resulting in a first sample ordinate value, wherein the first sample ordinate value is usable to determine at least a portion of a displayable image.

13. A method for computing sample ordinate values in a graphics system, the method comprising:

receiving graphics data including three vertices defining a triangle;

receiving sample positions which reside in a two-dimensional screen space;

computing a first axial rate of change of a first ordinate based on the three vertices, and, for each of said sample positions residing inside the triangle;

(a) multiplying the first axial rate by a first sample displacement resulting in a first product;

(b) interpolating a first projection value for a projection point on a first edge of the triangle; and

(c) adding the first product to the first projection value resulting in a first sample ordinate value, wherein said first sample ordinate value is usable to determine at least a portion of a displayable image.

22. A method comprising:

receiving graphics data including three vertices defining a triangle;

receiving samples which reside in a two-dimensional screen space;

computing a first minor axis ordinate difference along a minor axis of the triangle; and

computing a first sample ordinate value for each sample inside the triangle, wherein said computing the first sample ordinate value for a first sample inside the triangle includes;

(a) computing a minor axis positional fraction corresponding to the first sample;

(b) multiplying the minor axis positional fraction by the first minor axis ordinate difference to generate a first product; and

(c) adding the first product to one or more ordinate adjustment values to generate the first sample ordinate value, wherein the first sample ordinate value is usable to determine at least a portion of a pixel in a displayable image.

23. The method of claim 22, wherein said computing the first minor axis ordinate difference comprises:

interpolating an auxiliary ordinate value for an auxiliary point on a first edge of the triangle;

subtracting the auxiliary ordinate value from an ordinate value of an opposing vertex not on the first edge;

wherein the auxiliary point has the same major axis coordinate as the opposing vertex.

24. The method of claim 23, wherein said computing the minor axis positional fraction corresponding to the first sample comprises:

subtracting a minor axis coordinate of the auxiliary point from the minor axis coordinate of the opposing vertex to generate a minor axis positional difference;

multiplying a first minor axis sample displacement corresponding to the first sample by a reciprocal of the minor axis positional difference to generate said minor axis positional fraction.

25. The method of claim 24, wherein said first minor axis sample displacement is equal to a minor axis coordinate of said first sample minus a minor axis coordinate of a projection point on the first edge, wherein the projection point has the same major axis coordinate as the first sample.

26. The method of claim 22 further comprising computing a first edge ordinate difference for a first edge of the triangle, wherein said computing the first sample ordinate value for the first sample inside the triangle further includes:

(d) computing a major axis positional fraction corresponding to the first sample;

(e) multiplying the major axis positional fraction by the first edge ordinate difference to generate a first one of said one or more ordinate adjustment values, wherein an ordinate value of a first vertex bounding the first edge is a second one of said one or more ordinate adjustment values.

27. The method of claim 26, wherein said computing the first edge ordinate difference comprises subtracting an ordinate value for the first vertex from an ordinate value of a second vertex bounding the controlling edge.

28. The method of claim 26, wherein said computing the major axis positional fraction corresponding to the first sample comprises:

subtracting a major axis coordinate of the first vertex from a major axis coordinate of a second vertex bounding the first edge to generate a first edge major displacement;

subtracting a major axis coordinate of the first vertex from a major axis coordinate of the first sample to generate a sample-relative major axis displacement;

multiplying the sample-relative major axis displacement by the reciprocal of the controlling edge major displacement.

29. The method of claim 26 further comprising:

computing a horizontal edge displacement and a vertical edge displacement for each of the triangle edges;

determining a major displacement for each edge as the maximum of the horizontal edge displacement and a vertical edge displacement;

determining the first edge as the edge whose major displacement is greater than or equal to the major displacements for all other edges of the triangle.

30. The method of claim 22 further comprising:

operating on the first sample ordinate values corresponding to one or more samples to generate a pixel value; and

transmitting the pixel value to a display device.

31. A graphics system comprising:

sample position generation logic configured to generate sample positions in a two-dimensional screen space;

sample ordinate generation logic configured to receive graphics data including three vertices defining a triangle and ordinate data for each of the three vertices, and to compute a first minor axis ordinate difference along a minor axis of the triangle, wherein the rendering unit is further configured to compute a first sample ordinate value for a first sample position inside the triangle by;

(a) computing a minor axis positional fraction corresponding to the first sample position;

(b) multiplying the minor axis positional fraction by the first minor axis ordinate difference to generate a first product;

(c) adding the first product to one or more ordinate adjustment values to generate the first sample ordinate value, wherein the first sample ordinate value is usable to determine at least a portion of a pixel in a displayable image.

32. The graphics system of claim 31, wherein said sample ordinate generation logic is configured to compute the first minor axis ordinate difference by:

interpolating an auxiliary ordinate value for an auxiliary point on a first edge of the triangle;

subtracting the auxiliary ordinate value from an ordinate value of an opposing vertex not on the first edge;

wherein the auxiliary point has the same major axis coordinate as the opposing vertex.

33. The graphics system of claim 32, wherein said sample ordinate generation logic is configured to compute the minor axis positional fraction corresponding to the first sample by:

subtracting a minor axis coordinate of the auxiliary point from the minor axis coordinate of the opposing vertex to generate a minor axis positional difference;

multiplying a first minor axis sample displacement corresponding to the first sample position by a reciprocal of the minor axis positional difference to generate said minor axis positional fraction.

34. The graphics system of claim 33, wherein said first minor axis sample displacement is equal to a minor axis coordinate of said first sample position minus a minor axis coordinate of a projection point on the first edge, wherein the projection point has the same major axis coordinate as the first sample position.

35. The graphics system of claim 31, wherein said sample ordinate generation logic is further configured to compute a first edge ordinate difference for a first edge of the triangle, and to compute the first sample ordinate value for the first sample position inside the triangle by:

(d) computing a major axis positional fraction corresponding to the first sample;

(e) multiplying the major axis positional fraction by the first edge ordinate difference to generate a first one of said one or more ordinate adjustment values, wherein an ordinate value of a first vertex bounding the first edge is a second one of said one or more ordinate adjustment values.

36. The graphics system of claim 35, wherein said sample ordinate generation logic is configured to compute the first edge ordinate difference by subtracting an ordinate value for the first vertex from an ordinate value of a second vertex bounding the controlling edge.

37. The graphics system of claim 35, wherein said sample ordinate generation logic is configured to compute the major axis positional fraction corresponding to the first sample by:

multiplying a sample-relative major axis displacement by the reciprocal of a controlling edge major displacement,

wherein the first edge major displacement is a difference between a major axis coordinate of the first vertex and a major axis coordinate of a second vertex bounding the first edge,

wherein the sample-relative major axis displacement is a difference between a major axis coordinate of the first vertex and a major axis coordinate of the first sample.

38. The graphics system of claim 35 further comprising sample testing logic configured to:

compute a horizontal edge displacement and a vertical edge displacement for each of the triangle edges;

determine a major displacement for each edge as the maximum of the horizontal edge displacement and a vertical edge displacement; and

determine the first edge as the edge whose major displacement is greater than or equal to the major displacements for all other edges of the triangle.

39. The graphics system of claim 31 further comprising a sample-to-pixel calculation unit configured to operate on the first sample ordinate values corresponding to one or more of the sample positions to generate a pixel value, and to transmit the pixel value to a display device.

40. A rendering unit comprising:

position generation logic configured to generate pixel positions in a two-dimensional screen space;

testing logic configured to receive graphics data including three vertices defining a triangle and to determine which of said pixel positions reside inside the triangle;

ordinate generation logic coupled to the position generation logic and the testing logic, wherein the ordinate generation logic is configured to compute a first axial rate of change of a first ordinate based on the three vertices, and, for each pixel position residing inside the triangle, (a) to multiply the first axial rate by a first pixel displacement resulting in a first product, (b) to interpolate a first projection value for a projection point on a first edge of the triangle, and (c) to add the first product to the first projection value resulting in a first pixel ordinate value, wherein the first pixel ordinate value is usable to determine at least a portion of a displayable image.

41. A method for computing pixel ordinate values in a graphics system, the method comprising:

receiving graphics data including three vertices defining a triangle;

receiving pixel positions which reside in a two-dimensional screen space;

computing a first axial rate of change of a first ordinate based on the three vertices, and, for each of said pixel positions residing inside the triangle;

(a) multiplying the first axial rate by a first pixel displacement resulting in a first product;

(b) interpolating a first projection value for a projection point on a first edge of the triangle; and

(c) adding the first product to the first projection value resulting in a first pixel ordinate value, wherein said first pixel ordinate value is usable to determine at least a portion of a displayable image.