bezier package

Helper for Bézier Curves, Triangles, and Higher Order Objects.

Intended to perform basic operations on Bézier objects such as intersections, length / area / etc. computations, subdivision, implicitization and other relevant information.

Plotting utilities are also provided.

bezier.__version__ = '2023.7.28'

The current version of bezier.

Type:str

Submodules

• bezier.curve module
  • Curve
    • Curve.from_nodes()
    • Curve.length
    • Curve.copy()
    • Curve.evaluate()
    • Curve.evaluate_multi()
    • Curve.evaluate_hodograph()
    • Curve.plot()
    • Curve.subdivide()
    • Curve.intersect()
    • Curve.self_intersections()
    • Curve.elevate()
    • Curve.reduce_()
    • Curve.specialize()
    • Curve.locate()
    • Curve.to_symbolic()
    • Curve.implicitize()
    • Curve.degree
    • Curve.dimension
    • Curve.nodes
• bezier.curved_polygon module
  • CurvedPolygon
    • CurvedPolygon.num_sides
    • CurvedPolygon.area
    • CurvedPolygon.plot()
• bezier.triangle module
  • Triangle
    • Triangle.from_nodes()
    • Triangle.area
    • Triangle.edges
    • Triangle.evaluate_barycentric()
    • Triangle.evaluate_barycentric_multi()
    • Triangle.evaluate_cartesian()
    • Triangle.evaluate_cartesian_multi()
    • Triangle.plot()
    • Triangle.subdivide()
    • Triangle.is_valid
    • Triangle.locate()
    • Triangle.intersect()
    • Triangle.elevate()
    • Triangle.to_symbolic()
    • Triangle.implicitize()
    • Triangle.degree
    • Triangle.dimension
    • Triangle.nodes

Subpackages

• bezier.hazmat package
  • Submodules
    • bezier.hazmat.algebraic_intersection module
      • evaluate()
      • eval_intersection_polynomial()
      • to_power_basis()
      • polynomial_norm()
      • normalize_polynomial()
      • bernstein_companion()
      • bezier_roots()
      • lu_companion()
      • bezier_value_check()
      • roots_in_unit_interval()
      • intersect_curves()
      • poly_to_power_basis()
      • locate_point()
      • all_intersections()
    • bezier.hazmat.clipping module
      • compute_implicit_line()
      • compute_fat_line()
      • clip_range()
    • bezier.hazmat.curve_helpers module
      • make_subdivision_matrices()
      • subdivide_nodes()
      • evaluate_multi()
      • evaluate_multi_vs()
      • evaluate_multi_de_casteljau()
      • evaluate_multi_barycentric()
      • vec_size()
      • compute_length()
      • elevate_nodes()
      • de_casteljau_one_round()
      • specialize_curve()
      • evaluate_hodograph()
      • get_curvature()
      • newton_refine()
      • locate_point()
      • reduce_pseudo_inverse()
      • projection_error()
      • maybe_reduce()
      • full_reduce()
      • discrete_turning_angle()
    • bezier.hazmat.geometric_intersection module
      • bbox_intersect()
      • linearization_error()
      • segment_intersection()
      • parallel_lines_parameters()
      • line_line_collide()
      • convex_hull_collide()
      • from_linearized()
      • add_intersection()
      • endpoint_check()
      • tangent_bbox_intersection()
      • bbox_line_intersect()
      • intersect_one_round()
      • prune_candidates()
      • make_same_degree()
      • coincident_parameters()
      • check_lines()
      • all_intersections()
      • BoxIntersectionType
        • BoxIntersectionType.INTERSECTION
        • BoxIntersectionType.TANGENT
        • BoxIntersectionType.DISJOINT
      • SubdividedCurve
        • SubdividedCurve.nodes
        • SubdividedCurve.original_nodes
        • SubdividedCurve.start
        • SubdividedCurve.end
        • SubdividedCurve.subdivide()
      • Linearization
        • Linearization.curve
        • Linearization.error
        • Linearization.start_node
        • Linearization.end_node
        • Linearization.subdivide()
        • Linearization.from_shape()
      • self_intersections()
    • bezier.hazmat.helpers module
      • vector_close()
      • in_interval()
      • bbox()
      • contains_nd()
      • cross_product()
      • matrix_product()
      • wiggle_interval()
      • cross_product_compare()
      • in_sorted()
      • simple_convex_hull()
      • is_separating()
      • polygon_collide()
      • solve2x2()
      • UnsupportedDegree
        • UnsupportedDegree.degree
        • UnsupportedDegree.args
        • UnsupportedDegree.with_traceback()
        • UnsupportedDegree.supported
    • bezier.hazmat.intersection_helpers module
      • ZERO_THRESHOLD
      • MAX_NEWTON_ITERATIONS
      • NEWTON_ERROR_RATIO
      • newton_refine()
      • NewtonSimpleRoot
      • NewtonDoubleRoot
      • newton_iterate()
      • full_newton_nonzero()
      • full_newton()
      • IntersectionClassification
        • IntersectionClassification.FIRST
        • IntersectionClassification.SECOND
        • IntersectionClassification.OPPOSED
        • IntersectionClassification.TANGENT_FIRST
        • IntersectionClassification.TANGENT_SECOND
        • IntersectionClassification.IGNORED_CORNER
        • IntersectionClassification.TANGENT_BOTH
        • IntersectionClassification.COINCIDENT
        • IntersectionClassification.COINCIDENT_UNUSED
      • Intersection
        • Intersection.index_first
        • Intersection.s
        • Intersection.index_second
        • Intersection.t
        • Intersection.interior_curve
      • IntersectionStrategy
        • IntersectionStrategy.GEOMETRIC
        • IntersectionStrategy.ALGEBRAIC
    • bezier.hazmat.triangle_helpers module
      • polynomial_sign()
      • two_by_two_det()
      • quadratic_jacobian_polynomial()
      • cubic_jacobian_polynomial()
      • de_casteljau_one_round()
      • make_transform()
      • reduced_to_matrix()
      • specialize_triangle()
      • subdivide_nodes()
      • jacobian_s()
      • jacobian_t()
      • jacobian_both()
      • jacobian_det()
      • classify_tangent_intersection()
      • ignored_edge_corner()
      • ignored_double_corner()
      • ignored_corner()
      • classify_intersection()
      • handle_ends()
      • to_front()
      • get_next_first()
      • get_next_second()
      • get_next_coincident()
      • is_first()
      • is_second()
      • get_next()
      • ends_to_curve()
      • no_intersections()
      • tangent_only_intersections()
      • basic_interior_combine()
      • combine_intersections()
      • evaluate_barycentric()
      • evaluate_barycentric_multi()
      • evaluate_cartesian_multi()
      • compute_edge_nodes()
      • shoelace_for_area()
      • compute_area()
    • bezier.hazmat.triangle_intersection module
      • newton_refine_solve()
      • newton_refine()
      • update_locate_candidates()
      • mean_centroid()
      • locate_point()
      • same_intersection()
      • verify_duplicates()
      • verify_edge_segments()
      • add_edge_end_unused()
      • check_unused()
      • add_intersection()
      • classify_coincident()
      • should_use()
      • triangle_intersections()
      • generic_intersect()
      • geometric_intersect()
      • algebraic_intersect()