1.. _math utilities: 2 3.. module:: ezdxf.math 4 5Utility functions and classes located in module :mod:`ezdxf.math`. 6 7Functions 8========= 9 10.. autofunction:: closest_point 11 12.. autofunction:: uniform_knot_vector 13 14.. autofunction:: open_uniform_knot_vector 15 16.. autofunction:: required_knot_values 17 18.. autofunction:: xround 19 20.. autofunction:: linspace 21 22.. autofunction:: area 23 24.. autofunction:: arc_angle_span_deg 25 26.. autofunction:: ellipse_param_span 27 28.. _bulge_related_functions: 29 30Bulge Related Functions 31----------------------- 32 33.. seealso:: 34 35 Description of the :ref:`bulge value`. 36 37.. autofunction:: bulge_center 38 39.. autofunction:: bulge_radius 40 41.. autofunction:: arc_to_bulge 42 43.. autofunction:: bulge_to_arc 44 45.. autofunction:: bulge_3_points 46 472D Functions 48============ 49 50.. autofunction:: arc_segment_count 51 52.. autofunction:: arc_chord_length 53 54.. autofunction:: distance_point_line_2d(point: Vec2, start: Vec2, end: Vec2) -> float 55 56.. autofunction:: point_to_line_relation(point: Vec2, start: Vec2, end: Vec2, abs_tol=1e-10) -> int 57 58.. autofunction:: is_point_on_line_2d(point: Vec2, start: Vec2, end: Vec2, ray=True, abs_tol=1e-10) -> bool 59 60.. autofunction:: is_point_left_of_line(point: Vec2, start: Vec2, end: Vec2, colinear=False) -> bool 61 62.. autofunction:: is_point_in_polygon_2d(point: Vec2, polygon: Iterable[Vec2], abs_tol=1e-10) -> int 63 64.. autofunction:: convex_hull_2d 65 66.. autofunction:: intersection_line_line_2d(line1: Sequence[Vec2], line2: Sequence[Vec2], virtual=True, abs_tol=1e-10) -> Optional[Vec2] 67 68.. autofunction:: rytz_axis_construction(d1: Vec3, d2: Vec3) -> Tuple[Vec3, Vec3, float] 69 70.. autofunction:: clip_polygon_2d 71 72.. autofunction:: offset_vertices_2d 73 74.. code-block:: Python 75 76 source = [(0, 0), (3, 0), (3, 3), (0, 3)] 77 result = list(offset_vertices_2d(source, offset=0.5, closed=True)) 78 79.. image:: gfx/offset_vertices_2d_1.png 80 81Example for a closed collinear shape, which creates 2 additional vertices and the first one has an unexpected location: 82 83.. code-block:: Python 84 85 source = [(0, 0), (0, 1), (0, 2), (0, 3)] 86 result = list(offset_vertices_2d(source, offset=0.5, closed=True)) 87 88.. image:: gfx/offset_vertices_2d_2.png 89 903D Functions 91============ 92 93.. seealso:: 94 95 The free online book `3D Math Primer for Graphics and Game Development <https://gamemath.com/>`_ 96 is a very good resource for learning vector math and other graphic related topics, 97 it is easy to read for beginners and especially targeted to programmers. 98 99.. autofunction:: basic_transformation(move: Vertex = (0, 0, 0), scale: Vertex = (1, 1, 1), z_rotation: float = 0) -> Matrix44 100 101.. autofunction:: normal_vector_3p(a: Vec3, b: Vec3, c: Vec3) -> Vec3 102 103.. autofunction:: best_fit_normal(vertices: Iterable[Vertex]) -> Vec3 104 105.. autofunction:: is_planar_face(face: Sequence[Vec3], abs_tol=1e-9) -> bool 106 107.. autofunction:: subdivide_face(face: Sequence[Union[Vec3, Vec2]], quads=True) -> Iterable[List[Vec3]] 108 109.. autofunction:: subdivide_ngons(faces: Iterable[Sequence[Union[Vec3, Vec2]]]) -> Iterable[List[Vec3]] 110 111.. autofunction:: distance_point_line_3d(point: Vec3, start: Vec3, end: Vec3) -> float 112 113.. autofunction:: intersection_ray_ray_3d(ray1: Tuple[Vec3, Vec3], ray2: Tuple[Vec3, Vec3], abs_tol=1e-10) -> Sequence[Vec3] 114 115.. autofunction:: estimate_tangents(points: List[Vec3], method: str = '5-points', normalize = True) -> List[Vec3] 116 117.. autofunction:: estimate_end_tangent_magnitude(points: List[Vec3], method: str = 'chord') -> List[Vec3] 118 119.. autofunction:: fit_points_to_cad_cv 120 121.. autofunction:: fit_points_to_cubic_bezier 122 123.. autofunction:: global_bspline_interpolation 124 125.. autofunction:: local_cubic_bspline_interpolation(fit_points: Iterable[Vertex], method: str = '5-points', tangents :Iterable[Vertex] = None) -> BSpline 126 127.. autofunction:: rational_bspline_from_arc(center: Vec3 = (0, 0), radius:float=1, start_angle: float = 0, end_angle: float = 360, segments: int = 1) -> BSpline 128 129.. autofunction:: rational_bspline_from_ellipse(ellipse: ConstructionEllipse, segments: int = 1) -> BSpline 130 131.. autofunction:: open_uniform_bspline(control_points: Iterable[Vertex], order: int = 4, weights: Iterable[float] = None) -> BSpline 132 133.. autofunction:: closed_uniform_bspline(control_points: Iterable[Vertex], order: int = 4, weights: Iterable[float] = None) -> BSpline 134 135.. autofunction:: cubic_bezier_from_arc(center: Vec3 = (0, 0), radius:float=1, start_angle: float = 0, end_angle: float = 360, segments: int = 1) -> Iterable[Bezier4P] 136 137.. autofunction:: cubic_bezier_from_ellipse(ellipse: ConstructionEllipse, segments: int = 1) -> Iterable[Bezier4P] 138 139.. autofunction:: cubic_bezier_interpolation(points: Iterable[Vertex]) -> List[Bezier4P] 140 141.. autofunction:: quadratic_to_cubic_bezier(bezier: Bezier3P) -> Bezier4P 142 143.. autofunction:: bezier_to_bspline(Iterable[Union[Bezier3P, Bezier4P]], segments int = 4) -> BSpline 144 145.. autofunction:: have_bezier_curves_g1_continuity(b1: AnyBezier, b2 AnyBezier, g1_tol: float = 1e-4) -> bool 146 147Transformation Classes 148====================== 149 150OCS Class 151--------- 152 153.. autoclass:: OCS 154 155 .. autoattribute:: ux 156 157 .. autoattribute:: uy 158 159 .. autoattribute:: uz 160 161 .. automethod:: from_wcs 162 163 .. automethod:: points_from_wcs 164 165 .. automethod:: to_wcs 166 167 .. automethod:: points_to_wcs 168 169 .. automethod:: render_axis 170 171 172UCS Class 173--------- 174 175.. autoclass:: UCS 176 177 .. autoattribute:: ux 178 179 .. autoattribute:: uy 180 181 .. autoattribute:: uz 182 183 .. autoattribute:: is_cartesian 184 185 .. automethod:: copy() -> UCS 186 187 .. automethod:: to_wcs 188 189 .. automethod:: points_to_wcs 190 191 .. automethod:: direction_to_wcs 192 193 .. automethod:: from_wcs 194 195 .. automethod:: points_from_wcs 196 197 .. automethod:: direction_from_wcs 198 199 .. automethod:: to_ocs 200 201 .. automethod:: points_to_ocs 202 203 .. automethod:: to_ocs_angle_deg 204 205 .. automethod:: transform(m: Matrix44) -> UCS 206 207 .. automethod:: rotate(axis: Vertex, angle:float) -> UCS 208 209 .. automethod:: rotate_local_x(angle:float) -> UCS 210 211 .. automethod:: rotate_local_y(angle:float) -> UCS 212 213 .. automethod:: rotate_local_z(angle:float) -> UCS 214 215 .. automethod:: shift(delta: Vertex) -> UCS 216 217 .. automethod:: moveto(location: Vertex) -> UCS 218 219 .. automethod:: from_x_axis_and_point_in_xy 220 221 .. automethod:: from_x_axis_and_point_in_xz 222 223 .. automethod:: from_y_axis_and_point_in_xy 224 225 .. automethod:: from_y_axis_and_point_in_yz 226 227 .. automethod:: from_z_axis_and_point_in_xz 228 229 .. automethod:: from_z_axis_and_point_in_yz 230 231 .. automethod:: render_axis 232 233 234Matrix44 235-------- 236 237.. autoclass:: Matrix44 238 239 .. automethod:: __repr__ 240 241 .. automethod:: get_row 242 243 .. automethod:: set_row 244 245 .. automethod:: get_col 246 247 .. automethod:: set_col 248 249 .. automethod:: copy() -> Matrix44 250 251 .. automethod:: __copy__() -> Matrix44 252 253 .. automethod:: scale(sx: float, sy: float = None, sz: float = None) -> Matrix44 254 255 .. automethod:: translate(dx: float, dy: float, dz: float) -> Matrix44 256 257 .. automethod:: x_rotate(angle: float) -> Matrix44 258 259 .. automethod:: y_rotate(angle: float) -> Matrix44 260 261 .. automethod:: z_rotate(angle: float) -> Matrix44 262 263 .. automethod:: axis_rotate(axis: Vertex, angle: float) -> Matrix44 264 265 .. automethod:: xyz_rotate(angle_x: float, angle_y: float, angle_z: float) -> Matrix44 266 267 .. automethod:: shear_xy(angle_x: float, angle_y: float) -> Matrix44 268 269 .. automethod:: perspective_projection(left: float, right: float, top: float, bottom: float, near: float, far: float) -> Matrix44 270 271 .. automethod:: perspective_projection_fov(fov: float, aspect: float, near: float, far: float) -> Matrix44 272 273 .. automethod:: chain(*matrices: Iterable[Matrix44]) -> Matrix44 274 275 .. automethod:: ucs(ux: Vertex, uy: Vertex, uz: Vertex) -> Matrix44 276 277 .. automethod:: __hash__ 278 279 .. automethod:: __getitem__ 280 281 .. automethod:: __setitem__ 282 283 .. automethod:: __iter__ 284 285 .. automethod:: rows 286 287 .. automethod:: columns 288 289 .. automethod:: __mul__(other: Matrix44) -> Matrix44 290 291 .. automethod:: __imul__(other: Matrix44) -> Matrix44 292 293 .. automethod:: transform 294 295 .. automethod:: transform_direction 296 297 .. automethod:: transform_vertices 298 299 .. automethod:: transform_directions 300 301 .. automethod:: transpose 302 303 .. automethod:: determinant 304 305 .. automethod:: inverse 306 307Construction Tools 308================== 309 310Vec3 311---- 312 313.. autoclass:: Vec3 314 315 .. autoattribute:: x 316 317 .. autoattribute:: y 318 319 .. autoattribute:: z 320 321 .. autoattribute:: xy 322 323 .. autoattribute:: xyz 324 325 .. autoattribute:: vec2 326 327 .. autoattribute:: magnitude 328 329 .. autoattribute:: magnitude_xy 330 331 .. autoattribute:: magnitude_square 332 333 .. autoattribute:: is_null 334 335 .. autoattribute:: angle 336 337 .. autoattribute:: angle_deg 338 339 .. autoattribute:: spatial_angle 340 341 .. autoattribute:: spatial_angle_deg 342 343 .. automethod:: __str__ 344 345 .. automethod:: __repr__ 346 347 .. automethod:: __len__ 348 349 .. automethod:: __hash__ 350 351 .. automethod:: copy() -> Vec3 352 353 .. automethod:: __copy__() -> Vec3 354 355 .. automethod:: __deepcopy__(memodict: dict) -> Vec3 356 357 .. automethod:: __getitem__ 358 359 .. automethod:: __iter__ 360 361 .. automethod:: __abs__ 362 363 .. automethod:: replace(x: float = None, y: float = None, z: float = None) -> Vec3 364 365 .. automethod:: generate(items: Iterable[Vertex]) -> Iterable[Vec3] 366 367 .. automethod:: list(items: Iterable[Vertex]) -> List[Vec3] 368 369 .. automethod:: tuple(items: Iterable[Vertex]) -> Sequence[Vec3] 370 371 .. automethod:: from_angle(angle: float, length: float = 1.) -> Vec3 372 373 .. automethod:: from_deg_angle(angle: float, length: float = 1.) -> Vec3 374 375 .. automethod:: orthogonal(ccw: bool = True) -> Vec3 376 377 .. automethod:: lerp(other: Vertex, factor=.5) -> Vec3 378 379 .. automethod:: is_parallel(other: Vec3, abs_tolr=1e-12) -> bool 380 381 .. automethod:: project(other: Vertex) -> Vec3 382 383 .. automethod:: normalize(length: float = 1.) -> Vec3 384 385 .. automethod:: reversed() -> Vec3 386 387 .. automethod:: isclose 388 389 .. automethod:: __neg__() -> Vec3 390 391 .. automethod:: __bool__ 392 393 .. automethod:: __eq__ 394 395 .. automethod:: __lt__ 396 397 .. automethod:: __add__(other: Vertex) -> Vec3 398 399 .. automethod:: __radd__(other: Vertex) -> Vec3 400 401 .. automethod:: __sub__(other: Vertex) -> Vec3 402 403 .. automethod:: __rsub__(other: Vertex) -> Vec3 404 405 .. automethod:: __mul__(other: float) -> Vec3 406 407 .. automethod:: __rmul__(other: float) -> Vec3 408 409 .. automethod:: __truediv__(other: float) -> Vec3 410 411 .. automethod:: dot 412 413 .. automethod:: cross(other: Vertex) -> Vec3 414 415 .. automethod:: distance 416 417 .. automethod:: angle_about(base: Vec3, target: Vec3) -> float 418 419 .. automethod:: angle_between 420 421 .. automethod:: rotate(angle: float) -> Vec3 422 423 .. automethod:: rotate_deg(angle: float) -> Vec3 424 425 .. automethod:: sum(items: Iterable[Vertex]) -> Vec3 426 427.. attribute:: X_AXIS 428 429 :code:`Vec3(1, 0, 0)` 430 431.. attribute:: Y_AXIS 432 433 :code:`Vec3(0, 1, 0)` 434 435.. attribute:: Z_AXIS 436 437 :code:`Vec3(0, 0, 1)` 438 439.. attribute:: NULLVEC 440 441 :code:`Vec3(0, 0, 0)` 442 443Vec2 444---- 445 446.. autoclass:: Vec2 447 448Plane 449----- 450 451.. autoclass:: Plane(normal: Vec3, distance: float) 452 453 .. autoattribute:: normal 454 455 .. autoattribute:: distance_from_origin 456 457 .. autoattribute:: vector 458 459 .. automethod:: from_3p(a: Vec3, b: Vec3, c: Vec3) -> Plane 460 461 .. automethod:: from_vector(vector) -> Plane 462 463 .. automethod:: copy() -> Plane 464 465 .. automethod:: signed_distance_to(v: Vec3) -> float 466 467 .. automethod:: distance_to(v: Vec3) -> float 468 469 .. automethod:: is_coplanar_vertex(v: Vec3, abs_tol=1e-9) -> bool 470 471 .. automethod:: is_coplanar_plane(p: Plane, abs_tol=1e-9) -> bool 472 473 474BoundingBox 475----------- 476 477.. autoclass:: BoundingBox 478 479 .. attribute:: extmin 480 481 "lower left" corner of bounding box 482 483 .. attribute:: extmax 484 485 "upper right" corner of bounding box 486 487 .. autoproperty:: is_empty 488 489 .. autoproperty:: has_data 490 491 .. autoproperty:: size 492 493 .. autoproperty:: center 494 495 .. automethod:: inside 496 497 .. automethod:: any_inside 498 499 .. automethod:: all_inside 500 501 .. automethod:: intersect(other: BoundingBox) -> bool 502 503 .. automethod:: extend 504 505 .. automethod:: union(other: BoundingBox) -> BoundingBox 506 507 508BoundingBox2d 509------------- 510 511.. autoclass:: BoundingBox2d 512 513 .. attribute:: extmin 514 515 "lower left" corner of bounding box 516 517 .. attribute:: extmax 518 519 "upper right" corner of bounding box 520 521 .. autoproperty:: is_empty 522 523 .. autoproperty:: has_data 524 525 .. autoproperty:: size 526 527 .. autoproperty:: center 528 529 .. automethod:: inside 530 531 .. automethod:: any_inside 532 533 .. automethod:: all_inside 534 535 .. automethod:: intersect(other: BoundingBox2d) -> bool 536 537 .. automethod:: extend 538 539 .. automethod:: union(other: BoundingBox2d) -> BoundingBox2d 540 541ConstructionRay 542--------------- 543 544.. autoclass:: ConstructionRay 545 546 .. autoattribute:: location 547 548 .. autoattribute:: direction 549 550 .. autoattribute:: slope 551 552 .. autoattribute:: angle 553 554 .. autoattribute:: angle_deg 555 556 .. autoattribute:: is_vertical 557 558 .. autoattribute:: is_horizontal 559 560 .. automethod:: __str__ 561 562 .. automethod:: is_parallel(self, other: ConstructionRay) -> bool 563 564 .. automethod:: intersect(other: ConstructionRay) -> Vec2 565 566 .. automethod:: orthogonal(location: 'Vertex') -> ConstructionRay 567 568 .. automethod:: bisectrix(other: ConstructionRay) -> ConstructionRay: 569 570 .. automethod:: yof 571 572 .. automethod:: xof 573 574ConstructionLine 575---------------- 576 577.. autoclass:: ConstructionLine 578 579 .. attribute:: start 580 581 start point as :class:`Vec2` 582 583 .. attribute:: end 584 585 end point as :class:`Vec2` 586 587 .. autoattribute:: bounding_box 588 589 .. autoattribute:: ray 590 591 .. autoattribute:: is_vertical 592 593 .. autoattribute:: is_horizontal 594 595 .. automethod:: __str__ 596 597 .. automethod:: translate 598 599 .. automethod:: length 600 601 .. automethod:: midpoint() -> Vec2 602 603 .. automethod:: inside_bounding_box 604 605 .. automethod:: intersect(other: ConstructionLine, abs_tol:float=1e-10) -> Optional[Vec2] 606 607 .. automethod:: has_intersection(other: ConstructionLine, abs_tol:float=1e-10) -> bool 608 609 .. automethod:: is_point_left_of_line 610 611 612ConstructionCircle 613------------------ 614 615.. autoclass:: ConstructionCircle 616 617 .. attribute:: center 618 619 center point as :class:`Vec2` 620 621 .. attribute:: radius 622 623 radius as float 624 625 .. autoattribute:: bounding_box 626 627 .. automethod:: from_3p(p1: Vertex, p2: Vertex, p3: Vertex) -> ConstructionCircle 628 629 .. automethod:: __str__ 630 631 .. automethod:: translate 632 633 .. automethod:: point_at(angle: float) -> Vec2 634 635 .. automethod:: inside 636 637 .. automethod:: tangent(angle: float) -> ConstructionRay 638 639 .. automethod:: intersect_ray(ray: ConstructionRay, abs_tol: float = 1e-10) -> Sequence[Vec2] 640 641 .. automethod:: intersect_circle(other: ConstructionCircle, abs_tol: float = 1e-10) -> Sequence[Vec2] 642 643ConstructionArc 644--------------- 645 646.. autoclass:: ConstructionArc 647 648 .. attribute:: center 649 650 center point as :class:`Vec2` 651 652 .. attribute:: radius 653 654 radius as float 655 656 .. attribute:: start_angle 657 658 start angle in degrees 659 660 .. attribute:: end_angle 661 662 end angle in degrees 663 664 .. autoattribute:: angle_span 665 666 .. autoattribute:: start_angle_rad 667 668 .. autoattribute:: end_angle_rad 669 670 .. autoattribute:: start_point 671 672 .. autoattribute:: end_point 673 674 .. autoattribute:: bounding_box 675 676 .. automethod:: angles 677 678 .. automethod:: vertices 679 680 .. automethod:: tangents 681 682 .. automethod:: translate(dx: float, dy: float) -> ConstructionArc 683 684 .. automethod:: scale_uniform(s: float) -> ConstructionArc 685 686 .. automethod:: rotate_z(angle: float) -> ConstructionArc 687 688 .. automethod:: from_2p_angle(start_point: Vertex, end_point: Vertex, angle: float, ccw: bool = True) -> ConstructionArc 689 690 .. automethod:: from_2p_radius(start_point: Vertex, end_point: Vertex, radius: float, ccw: bool = True, center_is_left: bool = True) -> ConstructionArc 691 692 .. automethod:: from_3p(start_point: Vertex, end_point: Vertex, def_point: Vertex, ccw: bool = True) -> ConstructionArc 693 694 .. automethod:: add_to_layout(layout: BaseLayout, ucs: UCS = None, dxfattribs: dict = None) -> Arc 695 696ConstructionEllipse 697------------------- 698 699.. autoclass:: ConstructionEllipse 700 701 .. attribute:: center 702 703 center point as :class:`Vec3` 704 705 .. attribute:: major_axis 706 707 major axis as :class:`Vec3` 708 709 .. attribute:: minor_axis 710 711 minor axis as :class:`Vec3`, automatically calculated from 712 :attr:`major_axis` and :attr:`extrusion`. 713 714 .. attribute:: extrusion 715 716 extrusion vector (normal of ellipse plane) as :class:`Vec3` 717 718 .. attribute:: ratio 719 720 ratio of minor axis to major axis (float) 721 722 .. attribute:: start 723 724 start param in radians (float) 725 726 .. attribute:: end 727 728 end param in radians (float) 729 730 .. autoattribute:: start_point 731 732 .. autoattribute:: end_point 733 734 .. autoproperty:: param_span 735 736 .. automethod:: to_ocs() -> ConstructionEllipse 737 738 .. automethod:: params 739 740 .. automethod:: vertices 741 742 .. automethod:: flattening 743 744 .. automethod:: params_from_vertices 745 746 .. automethod:: dxfattribs 747 748 .. automethod:: main_axis_points 749 750 .. automethod:: from_arc(center: Vertex=(0, 0, 0), radius: float = 1, extrusion: Vertex=(0, 0, 1), start_angle: float = 0, end_angle: float = 360, ccw: bool = True) -> ConstructionEllipse 751 752 .. automethod:: transform(m: Matrix44) 753 754 .. automethod:: swap_axis 755 756 .. automethod:: add_to_layout(layout: BaseLayout, dxfattribs: dict = None) -> Ellipse 757 758 759ConstructionBox 760--------------- 761 762.. autoclass:: ConstructionBox 763 764 .. autoattribute:: center 765 766 .. autoattribute:: width 767 768 .. autoattribute:: height 769 770 .. autoattribute:: angle 771 772 .. autoattribute:: corners 773 774 .. autoattribute:: bounding_box 775 776 .. autoattribute:: incircle_radius 777 778 .. autoattribute:: circumcircle_radius 779 780 .. automethod:: __iter__() -> Iterable[Vec2] 781 782 .. automethod:: __getitem__(corner) -> Vec2 783 784 .. automethod:: __repr__ 785 786 .. automethod:: from_points(p1: Vertex, p2: Vertex) -> ConstructionBox 787 788 .. automethod:: translate 789 790 .. automethod:: expand 791 792 .. automethod:: scale 793 794 .. automethod:: rotate 795 796 .. automethod:: is_inside 797 798 .. automethod:: is_any_corner_inside(other: ConstructionBox) -> bool 799 800 .. automethod:: is_overlapping(other: ConstructionBox) -> bool 801 802 .. automethod:: border_lines() -> Sequence[ConstructionLine] 803 804 .. automethod:: intersect(line: ConstructionLine) -> List[Vec2] 805 806Shape2d 807------- 808 809.. autoclass:: Shape2d 810 811 .. attribute:: vertices 812 813 List of :class:`Vec2` objects 814 815 .. autoattribute:: bounding_box 816 817 .. automethod:: __len__ 818 819 .. automethod:: __getitem__(item) -> Vec2 820 821 .. automethod:: append 822 823 .. automethod:: extend 824 825 .. automethod:: translate 826 827 .. automethod:: scale 828 829 .. automethod:: scale_uniform 830 831 .. automethod:: rotate 832 833 .. automethod:: rotate_rad 834 835 .. automethod:: offset 836 837 .. automethod:: convex_hull 838 839Curves 840====== 841 842BSpline 843------- 844 845.. autoclass:: BSpline 846 847 .. autoproperty:: control_points 848 849 .. autoproperty:: count 850 851 .. autoproperty:: order 852 853 .. autoproperty:: degree 854 855 .. autoproperty:: max_t 856 857 .. autoproperty:: is_rational 858 859 .. autoproperty:: is_clamped 860 861 .. automethod:: knots 862 863 .. automethod:: weights 864 865 .. automethod:: params 866 867 .. automethod:: reverse() -> BSpline 868 869 .. automethod:: transform(m: Matrix44) -> BSpline 870 871 .. automethod:: approximate(segments: int = 20) -> Iterable[Vec3] 872 873 .. automethod:: flattening(distance: float, segments: int = 4) -> Iterable[Vec3] 874 875 .. automethod:: point(t: float) -> Vec3 876 877 .. automethod:: points(t: float) -> List[Vec3] 878 879 .. automethod:: derivative(t: float, n: int=2) -> List[Vec3] 880 881 .. automethod:: derivatives(t: Iterable[float], n: int=2) -> Iterable[List[Vec3]] 882 883 .. automethod:: insert_knot(t: float) -> BSpline 884 885 .. automethod:: knot_refinement(u: Iterable[flat]) -> BSpline 886 887 .. automethod:: from_ellipse(ellipse: ConstructionEllipse) -> BSpline 888 889 .. automethod:: from_arc(arc: ConstructionArc) -> BSpline 890 891 .. automethod:: from_fit_points(points: Iterable[Vertex], degree:int=3, method='chord') -> BSpline 892 893 .. automethod:: arc_approximation(arc: ConstructionArc, num:int=16) -> BSpline 894 895 .. automethod:: ellipse_approximation(ellipse: ConstructionEllipse, num:int=16) -> BSpline 896 897 .. automethod:: bezier_decomposition() -> Iterable[List[Vec3]] 898 899 .. automethod:: cubic_bezier_approximation(level: int = 3, segments: int = None) -> Iterable[Bezier4P] 900 901 902Bezier 903------ 904 905.. autoclass:: Bezier 906 907 .. autoattribute:: control_points 908 909 .. automethod:: params 910 911 .. automethod:: reverse() -> Bezier 912 913 .. automethod:: transform(m: Matrix44) -> Bezier 914 915 .. automethod:: approximate(segments: int = 20) -> Iterable[Vec3] 916 917 .. automethod:: flattening(distance: float, segments: int=4) -> Iterable[Vec3] 918 919 .. automethod:: point(t: float) -> Vec3 920 921 .. automethod:: points(t: Iterable[float]) -> Iterable[Vec3] 922 923 .. automethod:: derivative(t: float) -> Tuple[Vec3, Vec3, Vec3] 924 925 .. automethod:: derivatives(t: Iterable[float]) -> Iterable[Tuple[Vec3, Vec3, Vec3]] 926 927 928Bezier4P 929-------- 930 931.. autoclass:: Bezier4P 932 933 .. autoattribute:: control_points 934 935 .. automethod:: reverse() -> Bezier4P 936 937 .. automethod:: transform(m: Matrix44) -> Bezier4P 938 939 .. automethod:: approximate(segments: int) -> Iterable[Union[Vec3, Vec2]] 940 941 .. automethod:: flattening(distance: float, segments: int=4) -> Iterable[Union[Vec3, Vec2]] 942 943 .. automethod:: approximated_length 944 945 .. automethod:: point(t: float) -> Union[Vec3, Vec2] 946 947 .. automethod:: tangent(t: float) -> Union[Vec3, Vec2] 948 949Bezier3P 950-------- 951 952.. autoclass:: Bezier3P 953 954 .. autoattribute:: control_points 955 956 .. automethod:: reverse() -> Bezier3P 957 958 .. automethod:: transform(m: Matrix44) -> Bezier3P 959 960 .. automethod:: approximate(segments: int) -> Iterable[Union[Vec3, Vec2]] 961 962 .. automethod:: flattening(distance: float, segments: int=4) -> Iterable[Union[Vec3, Vec2]] 963 964 .. automethod:: approximated_length 965 966 .. automethod:: point(t: float) -> Union[Vec3, Vec2] 967 968 .. automethod:: tangent(t: float) -> Union[Vec3, Vec2] 969 970 971 972BezierSurface 973------------- 974 975.. autoclass:: BezierSurface 976 977 .. autoattribute:: nrows 978 979 .. autoattribute:: ncols 980 981 .. automethod:: point 982 983 .. automethod:: approximate 984 985 986EulerSpiral 987----------- 988 989.. autoclass:: EulerSpiral 990 991 .. automethod:: radius 992 993 .. automethod:: tangent(t: float) -> Vec3 994 995 .. automethod:: distance 996 997 .. automethod:: point(t: float) -> Vec3 998 999 .. automethod:: circle_center(t: float) -> Vec3 1000 1001 .. automethod:: approximate(length: float, segments: int) -> Iterable[Vec3] 1002 1003 .. automethod:: bspline(length: float, segments: int = 10, degree: int = 3, method: str = 'uniform') -> BSpline 1004 1005Linear Algebra 1006============== 1007 1008Functions 1009--------- 1010 1011.. autofunction:: gauss_jordan_solver(A: Iterable[Iterable[float]], B: Iterable[Iterable[float]]) -> Tuple[Matrix, Matrix] 1012 1013.. autofunction:: gauss_jordan_inverse(A: Iterable[Iterable[float]]) -> Matrix 1014 1015.. autofunction:: gauss_vector_solver 1016 1017.. autofunction:: gauss_matrix_solver(A: Iterable[Iterable[float]], B: Iterable[Iterable[float]]) -> Matrix 1018 1019.. autofunction:: tridiagonal_vector_solver(A: Iterable[Iterable[float]], B: Iterable[float]) -> List[float] 1020 1021.. autofunction:: tridiagonal_matrix_solver(A: Iterable[Iterable[float]], B: Iterable[Iterable[float]]) -> Matrix 1022 1023.. autofunction:: banded_matrix(A: Matrix, check_all=True) -> Tuple[int, int] 1024 1025.. autofunction:: detect_banded_matrix(A: Matrix, check_all=True) -> Tuple[int, int] 1026 1027.. autofunction:: compact_banded_matrix(A: Matrix, m1: int, m2: int) -> Matrix 1028 1029.. autofunction:: freeze_matrix(A: Union[MatrixData, Matrix]) -> Matrix 1030 1031Matrix Class 1032------------ 1033 1034.. autoclass:: Matrix 1035 1036 .. autoattribute:: nrows 1037 1038 .. autoattribute:: ncols 1039 1040 .. autoattribute:: shape 1041 1042 .. automethod:: reshape 1043 1044 .. automethod:: identity 1045 1046 .. automethod:: row 1047 1048 .. automethod:: iter_row 1049 1050 .. automethod:: col 1051 1052 .. automethod:: iter_col 1053 1054 .. automethod:: diag 1055 1056 .. automethod:: iter_diag 1057 1058 .. automethod:: rows 1059 1060 .. automethod:: cols 1061 1062 .. automethod:: set_row 1063 1064 .. automethod:: set_col 1065 1066 .. automethod:: set_diag 1067 1068 .. automethod:: append_row 1069 1070 .. automethod:: append_col 1071 1072 .. automethod:: swap_rows 1073 1074 .. automethod:: swap_cols 1075 1076 .. automethod:: transpose() -> Matrix 1077 1078 .. automethod:: inverse() -> Matrix 1079 1080 .. automethod:: determinant 1081 1082 .. automethod:: freeze() -> Matrix 1083 1084 .. automethod:: lu_decomp() -> LUDecomposition 1085 1086 .. automethod:: __getitem__(item: Tuple[int, int]) -> float 1087 1088 .. automethod:: __setitem__(item: Tuple[int, int], value: float) 1089 1090 .. automethod:: __eq__(other: Matrix) -> bool 1091 1092 .. automethod:: __add__(other: Union[Matrix, float]) -> Matrix 1093 1094 .. automethod:: __sub__(other: Union[Matrix, float]) -> Matrix 1095 1096 .. automethod:: __mul__(other: Union[Matrix, float]) -> Matrix 1097 1098 1099LUDecomposition Class 1100--------------------- 1101 1102.. autoclass:: LUDecomposition 1103 1104 .. autoattribute:: nrows 1105 1106 .. automethod:: solve_vector 1107 1108 .. automethod:: solve_matrix(B: Iterable[Iterable[float]]) -> Matrix 1109 1110 .. automethod:: inverse() -> Matrix 1111 1112 .. automethod:: determinant 1113 1114BandedMatrixLU Class 1115-------------------- 1116 1117.. autoclass:: BandedMatrixLU 1118 1119 .. attribute:: upper 1120 1121 Upper triangle 1122 1123 .. attribute:: lower 1124 1125 Lower triangle 1126 1127 .. attribute:: m1 1128 1129 Lower band count, excluding main matrix diagonal 1130 1131 .. attribute:: m2 1132 1133 Upper band count, excluding main matrix diagonal 1134 1135 .. attribute:: index 1136 1137 Swapped indices 1138 1139 .. autoattribute:: nrows 1140 1141 .. automethod:: solve_vector 1142 1143 .. automethod:: solve_matrix(B: Iterable[Iterable[float]]) -> Matrix 1144 1145 .. automethod:: determinant 1146 1147.. _Global Curve Interpolation: http://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/INT-APP/CURVE-INT-global.html 1148.. _uniform: https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/INT-APP/PARA-uniform.html 1149.. _chord length: https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/INT-APP/PARA-chord-length.html 1150.. _centripetal: https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/INT-APP/PARA-centripetal.html 1151.. _knot: http://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/INT-APP/PARA-knot-generation.html 1152.. _clamped curve: http://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve.html 1153.. _open curve: http://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve-open.html 1154.. _closed curve: http://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve-closed.html 1155.. _basis: http://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-basis_vector.html 1156.. _B-spline: https://en.wikipedia.org/wiki/B-spline 1157.. _Bézier curve: https://en.wikipedia.org/wiki/B%C3%A9zier_curve 1158.. _Lee Mac: http://www.lee-mac.com/bulgeconversion.html 1159.. _Gauss-Jordan: https://en.wikipedia.org/wiki/Gaussian_elimination 1160.. _Gauss-Elimination: https://en.wikipedia.org/wiki/Gaussian_elimination 1161.. _LU Decomposition: https://en.wikipedia.org/wiki/LU_decomposition 1162.. _sagitta: https://en.wikipedia.org/wiki/Sagitta_(geometry)
