1. A method comprising: defining in a rendering engine a rectangular area of pixels that bounds an entire triangular area of the pixels that defines a triangle to be rendered, wherein the rendering engine is implemented as one or more application-specific integrated circuits (ASICs); selecting in the rendering engine a line of pixels within the rectangular area of pixels; sequentially evaluating in the rendering engine coordinates associated with the pixels of the line of pixels starting at one end of the rectangular area to determine whether the pixels fall within the triangular area, wherein the one end of the rectangular area is common for the sequential evaluation of each line of pixels; ceasing in the rendering engine evaluation of the coordinates associated with the pixels of the line of pixels upon determining that at least one pixel of the line falls within the triangular area and a current pixel no longer falls within the triangular area; and updating in the rendering engine pixel data for the pixels that fall within the triangular area to render the triangular area, wherein updating pixel data comprises computing pixel data for the pixels of the rectangular area that fall within the triangular area in accordance with a set of linear equations that describe one or more attributes associated with the triangular area, computing an inverse coefficient matrix M −1 for computing linear coefficients of the set of linear equations, and applying the linear coefficients to each of the pixels that falls within the triangular area to compute an attribute value for each of the pixels, wherein applying the inverse coefficient matrix M −1 comprises applying the inverse coefficient matrix M −1 to compute the linear coefficients A, B, and C, for an attribute associated with vertices v 0 (x 0 ,y 0 ), v 1 (x 1 ,y 1 ), and v 2 (x 2 ,y 2 ) of the triangle as: [ A B C ] = M - 1 ⁡ [ v o v 1 v 2 ] , where a coefficient matrix M equals: M = [ x 0 y 0 1 x 1 y 1 1 x 2 y 2 1 ] , where the inverse coefficient matrix M −1 equals: M - 1 = 1 det ⁡ ( M ) ⁢ M C T , where det(M) equals: 
 det( M )=| M|=x 1 y 2 +x 2 y 0 +x 0 y 1 −x 2 y 1 −x 0 y 2 −x 1 y 0 , where M T C is a transpose of matrix M C , where matrix M c equals: M c = [ y 1 - y 2 x 2 - x 1 x 1 ⁢ y 2 - x 2 ⁢ y 1 y 2 - y 0 x 0 - x 2 x 2 ⁢ y 0 - x 0 ⁢ y 2 y 0 - y 1 x 1 - x 0 x 0 ⁢ y 1 - x 1 ⁢ y 0 ] ⁢ ⁢ and an attribute value for each pixel (X c , Y c ) is computed as 
 v=AX c +BY c +C.