This work presents a novel description of texture mapping polygons in a geometric view about scanlines and a simplified mapping function to improve the performance. The conventional perspective-correct mapping requires costly division operations. In this work, two concepts in perspective geometry, cross-ratio and vanishing point, are exploited to simplify the mapping function. We substitute the point at infinity on scanline into the cross-ratio equation, then obtain a simple description of perspective mapping in polygons. Our mapping function allows the spatial mapping of a pixel from a scanline on a screen plane to a texture plane taking only one division, one multiplication and three additions. The proposed algorithm speeds up the mapping process without losing any correctness. Experimental results indicate that the performance of proposed method is superior to other correct mapping methods.