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Many different algorithms have been developed. The simplest case is a line clipping by a convex polygon in <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$${E^{2}}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>E<\/mml:mi>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> with <jats:italic>O(N)<\/jats:italic> computational complexity and with known polygon edges orientation. This contribution presents a new algorithm for a line clipping by a convex polygon in E<jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$^{2}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow\/>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> with <jats:italic>O(lg N)<\/jats:italic> complexity, which is based on the point-in-half plane test. The proposed algorithm does not require prior knowledge of the polygon edge orientation. The vertices of the convex polygon and the clipped line can be given in projective space using homogeneous coordinates. The algorithm uses vector\u2013vector operations for efficient implementation with SSE or AVX vector\u2013vector instructions or on GPUs. 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