
{"publication_number": "US-9082228-B2", "abstract": "a rasterizer , based on time - dependent edge equations , computes analytical visibility in order to render accurate motion blur . an oracle - based compression algorithm for the time intervals lowers the frame buffer requirements . high quality motion blurred scenes can be rendered using a rasterizer with rather low memory requirements . the resulting images may contain motion blur for both opaque and transparent objects .", "application_number": "US-201113004928-A", "description": "the motion blur visibility problem may be solved analytically in order to avoid sampling noise . one embodiment involves rasterization of motion - blurred triangles with analytical visibility . however , a planar polygon with n number of vertices may be used . assume that the entire transform matrix , including projection , for a vertex is called m . a vertex in homogeneous clip space is then obtained as | p = m p , where p is the vertex in three - dimensional object space , and p is the resulting four - dimensional vertex in homogeneous clip space , i . e ., before division by the w - component . to simplify the derivation , we use the following notation : { circumflex over ( p )