Intersecting is an important factor which influences the effociency androbustness of Boolean algorithms in solid modeling based on surved-surfaces,andintersecting algorithms are closely related to geometric representa...Intersecting is an important factor which influences the effociency androbustness of Boolean algorithms in solid modeling based on surved-surfaces,andintersecting algorithms are closely related to geometric representations of curved-surfaces.Although surfaces can be commonly represented with NURBS,unnecessary complexitiesare caused in the intersecting of quadric surfaces.Quadrics are frequently used to des-cribe geometric features of shafts,holes and grooves etc.in mechanical part designing,therefore;their intersection algorithms are required to have higher accuracy,higher efficiency and higher robustness.For this reason,a practical representation ofquadric surfaces is studied in detail,and on the basis of that,algorithms of intersectingpoints are developed between quadric suraces and their boundaies,i.e.,conics,quarticnonplanar space curves.展开更多
We construct two conical surfaces which take non-coplanar lines as generatrix and rational Bezier curve as ridge-line, and prove that the intersecting line of conical surface has similar properties to Bezier curve. Th...We construct two conical surfaces which take non-coplanar lines as generatrix and rational Bezier curve as ridge-line, and prove that the intersecting line of conical surface has similar properties to Bezier curve. Then, the smoothly blending of two cylinders whose axes are non-coplanar is realized by taking intersecting line of conical surface as axes.展开更多
in the design of civil and water conservancy projects, the identical slope suffice isfrequently used. Its mathematical model may be formulated as an envelope of a cone when itS vertexmoves along the cylindrical helix....in the design of civil and water conservancy projects, the identical slope suffice isfrequently used. Its mathematical model may be formulated as an envelope of a cone when itS vertexmoves along the cylindrical helix. According to the principle of conStrUcting the envelope curves of afamily of circles, the parametric equstion for the identical slope surface is established. The parametricform makes it most convenient to draw the contour lines and grade lines, and is well suited toproduce indexed projection of identical slope surface in civil and water conservancy projects.展开更多
Let X be a complex projective algebraic manifold of dimension 2 and let D1,..., Du be distinct irreducible divisors on X such that no three of them share a common point. Let f: C → X\(U1≤i≤uDi) be a holomorphic map...Let X be a complex projective algebraic manifold of dimension 2 and let D1,..., Du be distinct irreducible divisors on X such that no three of them share a common point. Let f: C → X\(U1≤i≤uDi) be a holomorphic map. Assume that u ≥ 4 and that there exist positive integers n1,...,nu, c such that ninj(Di.Dj) = c for all pairs i, j. Then f is algebraically degenerate, i.e. its image is contained in an algebraic curve on X.展开更多
文摘Intersecting is an important factor which influences the effociency androbustness of Boolean algorithms in solid modeling based on surved-surfaces,andintersecting algorithms are closely related to geometric representations of curved-surfaces.Although surfaces can be commonly represented with NURBS,unnecessary complexitiesare caused in the intersecting of quadric surfaces.Quadrics are frequently used to des-cribe geometric features of shafts,holes and grooves etc.in mechanical part designing,therefore;their intersection algorithms are required to have higher accuracy,higher efficiency and higher robustness.For this reason,a practical representation ofquadric surfaces is studied in detail,and on the basis of that,algorithms of intersectingpoints are developed between quadric suraces and their boundaies,i.e.,conics,quarticnonplanar space curves.
文摘We construct two conical surfaces which take non-coplanar lines as generatrix and rational Bezier curve as ridge-line, and prove that the intersecting line of conical surface has similar properties to Bezier curve. Then, the smoothly blending of two cylinders whose axes are non-coplanar is realized by taking intersecting line of conical surface as axes.
文摘in the design of civil and water conservancy projects, the identical slope suffice isfrequently used. Its mathematical model may be formulated as an envelope of a cone when itS vertexmoves along the cylindrical helix. According to the principle of conStrUcting the envelope curves of afamily of circles, the parametric equstion for the identical slope surface is established. The parametricform makes it most convenient to draw the contour lines and grade lines, and is well suited toproduce indexed projection of identical slope surface in civil and water conservancy projects.
文摘Let X be a complex projective algebraic manifold of dimension 2 and let D1,..., Du be distinct irreducible divisors on X such that no three of them share a common point. Let f: C → X\(U1≤i≤uDi) be a holomorphic map. Assume that u ≥ 4 and that there exist positive integers n1,...,nu, c such that ninj(Di.Dj) = c for all pairs i, j. Then f is algebraically degenerate, i.e. its image is contained in an algebraic curve on X.
