Computing illumination of an elongated shape having a noncircular cross section

At least one computer-readable storage medium carrying instructions, which, when executed by at least one data processor of a system, cause the system to:

• obtain an indication of a shape of a noncircular cross-section of an elongated shape, and an orientation of the shape;
• based on the shape of the noncircular cross-section of the elongated shape and the orientation of the shape, create a nonuniform distribution of numbers mapping a uniform distribution of numbers to multiple points on a surface of the elongated shape;
• obtain an input value selected from the uniform distribution of numbers;
• map the input value to the nonuniform distribution of numbers to obtain a number among the nonuniform distribution of numbers;
• map the number among the nonuniform distribution of numbers to a point among the multiple points on the surface of the elongated shape;
• and
• calculate a normal of the elongated shape at the point among the multiple points on the surface of the elongated shape by applying a function to the input value selected from the uniform distribution of numbers.

A system comprising:

• at least one hardware processor;
• and
• at least one non-transitory memory storing instructions, which, when executed by the at least one hardware processor, cause the system to:
• obtain an indication of a shape of a noncircular cross-section of an elongated shape, and an orientation of the shape;
• based on the shape of the noncircular cross-section of the elongated shape and the orientation of the shape, create a nonuniform distribution of numbers mapping a uniform distribution of numbers to multiple points on a surface of the elongated shape;
• obtain an input value selected from the uniform distribution of numbers;
• map the input value to a number among the nonuniform distribution of numbers;
• map the number among the nonuniform distribution of numbers to a point among the multiple points on the surface of the elongated shape;
• and
• calculate a normal of the elongated shape at the point among the multiple points on the surface of the elongated shape by applying a function to the input value selected from the uniform distribution of numbers.