bezier.hazmat package

The bezier.hazmat subpackage is a “hazardous materials” layer.

The modules contained here provide low-level functionality for the public API of the bezier package. They are not subject to any API stability guarantees. Understanding these low-level details is not required to be an everyday user of bezier, but documenting them will allow examples and narrative for those interested on learning more.

In many cases, the code is a pure-Python implementation of functions provided in the binary extension speedup.

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.add_note()
    • 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()