1. A method that performs immediate Boolean Operations using geometric facets implemented in a computer system and operating with a computer, the method comprising: mapping rendering facets to extended triangles that contain neighbors; searching for the first pair of triangles that hold a start point of an intersection line by detecting whether two minimum bounding boxes overlap and performing edge-triangle intersection; extending the intersection lines until they get closed by searching neighboring triangles or all triangles are traversed; splitting triangles through which intersection lines pass; checking each triangle is obscure or visible; regrouping facets, deleting, and reserving triangles according to Boolean operation types; and mapping extended triangles to rendering facets.