Level of detail via numerically stable eigenvalue technology
Methods, systems and apparatuses may provide for technology that determines a major axis length of an ellipse in texture space based on a transformation matrix associated with a circle in screen space, inverts the major axis length, determines a product between the inverted major axis length and a determinant of the transformation matrix, and determines a minor axis length based on a modulus of the product between the inverted major axis length and the determinant of the transformation matrix. In one example, the technology selects a level of detail in the texture space based on the major axis length, the minor axis length, a direction of the major axis length, and a direction of the minor axis length.
1. A computing system comprising:
a display including a screen space; and
a graphics processor including logic coupled to one or more substrates, the logic to:
determine a major axis length of an ellipse in texture space based on a transformation matrix associated with a circle in the screen space,
invert the major axis length,
determine a product between the inverted major axis length and a determinant of the transformation matrix, and
determine a minor axis length based on a modulus of the product between the inverted major axis length and the determinant of the transformation matrix,
select a level of detail in the texture space based on the major axis length, the minor axis length, a direction of the major axis length, and a direction of the minor axis length, and
generate an interpolated texture in a graphics pipeline based on the level of detail.
2. The computing system of claim 1 , wherein to determine the major axis length, the logic is to:
determine a sum of squares value based on the transformation matrix, and
determine the determinant of the transformation matrix.
3. The computing system of claim 2 , wherein to determine the major axis length, the logic is further to determine a square root of a sum between the sum of squares value and two times the determinant.
4. The computing system of claim 2 , wherein to determine the major axis length, the logic is further to determine a square root of a difference between the sum of squares value and two times the determinant.
5. The computing system of claim 1 , wherein the logic is further to determine the direction of the major axis length based on one or more eigenvalue matrices.
6. The computing system of claim 5 , wherein the logic is further to determine the direction of the minor axis length based on the major axis length.
7. A semiconductor apparatus comprising:
one or more substrates; and
logic coupled to the one or more substrates, wherein the logic is implemented at least partly in one or more of configurable or fixed-functionality hardware, the logic to:
determine a major axis length of an ellipse in texture space based on a transformation matrix associated with a circle in screen space;
invert the major axis length;
determine a product between the inverted major axis length and a determinant of the transformation matrix;
determine a minor axis length based on a modulus of the product between the inverted major axis length and the determinant of the transformation matrix;
select a level of detail in the texture space based on the major axis length, the minor axis length, a direction of the major axis length, and a direction of the minor axis length; and
generate an interpolated texture in a graphics pipeline based on the level of detail.
8. The semiconductor apparatus of claim 7 , wherein to determine the major axis length, the logic is to:
determine a sum of squares value based on the transformation matrix; and
determine the determinant of the transformation matrix.
9. The semiconductor apparatus of claim 8 , wherein to determine the major axis length, the logic is further to determine a square root of a sum between the sum of squares value and two times the determinant.
10. The semiconductor apparatus of claim 8 , wherein to determine the major axis length, the logic is further to determine a square root of a difference between the sum of squares value and two times the determinant.
11. The semiconductor apparatus of claim 7 , wherein the logic is further to determine the direction of the major axis length based on one or more eigenvalue matrices.
12. The semiconductor apparatus of claim 11 , wherein the logic is further to determine the direction of the minor axis length based on the major axis length.
13. A method comprising:
determining, by a hardware processor, a major axis length of an ellipse in texture space based on a transformation matrix associated with a circle in screen space;
inverting, by the hardware processor, the major axis length;
determining, by the hardware processor, a product between the inverted major axis length and a determinant of the transformation matrix;
determining, by the hardware processor, a minor axis length based on a modulus of the product between the inverted major axis length and the determinant of the transformation matrix;
selecting a level of detail in the texture space based on the major axis length, the minor axis length, a direction of the major axis length, and a direction of the minor axis length; and
generating an interpolated texture in a graphics pipeline based on the level of detail.
14. The method of claim 13 , wherein determining the major axis length includes:
determining a sum of squares value based on the transformation matrix; and
determining the determinant of the transformation matrix.
15. The method of claim 14 , wherein determining the major axis length further includes determining a square root of a sum between the sum of squares value and two times the determinant.
16. The method of claim 14 , wherein determining the major axis length further includes determining a square root of a difference between the sum of squares value and two times the determinant.
17. The method of claim 13 , further including determining the direction of the major axis length based on one or more eigenvalue matrices.
18. The method of claim 17 , further including determining the direction of the minor axis length based on the major axis length.