Patent Document ID: 9305370
Application ID: 14193139
Patent Status: 1

Claim One:
1. A method of rendering graphical objects or shapes, the method comprising: determining which surface equations of a plurality of surface equations defined in ray parameters for respective ones of a plurality of implicit surfaces have real-root values, wherein a real-root value for each of the respective surface equations is a value that includes no imaginary component that when substituted into the respective surface equations causes the result of the respective surface equations to equal zero, wherein the plurality of implicit surfaces together form a graphical object or shape, and wherein determining which surface equations for respective ones of the plurality of implicit surfaces have real-root values comprises: determining which implicit surfaces are uncomplemented surfaces and which implicit surfaces are complemented surfaces, wherein an uncomplemented surface is an implicit surfaces from which another implicit surface is subtracted, and wherein a complemented surface is an implicit surface that is subtracted from another implicit surface; and determining whether surface equations for the complemented surfaces have real-root values and whether surface equations for the complemented surfaces do not have real-root values; determining a maximum real-root value from among a set of real-root values for the surface equations for the uncomplemented surfaces if the surface equations for the uncomplemented surface do not have real-root values; determining an intersection point of a ray associated with a pixel with the graphical object or shape based on the determined maximum real-root value; and rendering the pixel based on the determined intersection point.