Skip to content

Geometry#

This contains some utilities for adding geometry to an IDF.

Geometry utilities for the UBEM construction.

ShoeboxGeometry #

Bases: BaseModel

A simple shoebox constructor for the IDF model.

Can create gables, basements, and various zoning strategies.

Source code in epinterface/geometry.py
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
class ShoeboxGeometry(BaseModel):
    """A simple shoebox constructor for the IDF model.

    Can create gables, basements, and various zoning strategies.
    """

    x: float
    y: float
    w: float
    d: float
    h: float
    num_stories: int = Field(
        ...,
        title="Number of stories",
        ge=1,
        description="The number of stories in the building.",
    )
    zoning: ZoningType = Field(
        ...,
        title="Zoning type",
        description="Whether to use core/perim or full-floor zones.",
    )
    perim_depth: float = Field(
        default=3,
        title="Perimeter depth",
        description="Sets the perimeter depth when using core/perim zoning.  Ignored otherwise.",
    )
    roof_height: float | None = Field(
        default=None,
        title="Roof gable height",
        description="The height of the roof gable.  If None, a flat roof is assumed.",
    )
    basement: bool = Field(
        default=False,
        title="Basement",
        description="Whether or not to use a basement with same f2f height as building.",
    )
    exposed_basement_frac: float = Field(
        default=0.0,
        title="Exposed basement fraction",
        description="The fraction of the basement that is exposed.",
        ge=0,
        lt=1,
    )
    wwr: float = Field(
        default=0.15,
        title="Window-to-wall ratio",
        description="The window-to-wall ratio of the building.",
        ge=0,
        le=1,
    )

    @property
    def basement_storey_count(self) -> int:
        """Return the number of basement stories."""
        return 1 if self.basement else 0

    @property
    def attic_storey_count(self) -> int:
        """Return the number of attic stories."""
        return 1 if self.roof_height else 0

    @property
    def zones_height(self) -> float:
        """Return the total height of the zones, excluding any gabling."""
        return self.h * (self.num_stories)

    @property
    def total_height_with_gabling(self) -> float:
        """Return the total height of the building, including any gabling."""
        return self.zones_height + (self.roof_height or 0)

    @property
    def footprint_area(self) -> float:
        """Return the total floor area of the building."""
        return self.w * self.d

    @property
    def total_living_area(self) -> float:
        """Return the total living area of the building (does not include attic/basement)."""
        return self.footprint_area * self.num_stories

    @property
    def total_area(self) -> float:
        """Return the total area of the building."""
        return (
            self.total_living_area
            + self.footprint_area * self.basement_storey_count
            + self.footprint_area * (1 if self.roof_height else 0)
        )

    @property
    def basement_suffix(self) -> str:
        """Return the basement suffix for the building."""
        if not self.basement:
            msg = "Building has no basement."
            raise ValueError(msg)
        return "Storey 0" if self.zoning == "core/perim" else "Storey -1"

    @property
    def zones_per_storey(self) -> int:
        """Return the number of zones per storey."""
        if self.zoning == "core/perim":
            return 5
        else:
            return 1

    def add(self, idf: IDF) -> IDF:  # noqa: C901
        """Constructs a simple shoebox geometry in the IDF model.

        Takes advantage of the geomeppy methods to do so.

        Can create gables, basements, and various zoning strategies.

        Args:
            idf: The IDF model to add the geometry to.

        Returns:
            The IDF model with the added geometry.
        """
        lower_left_corner = (self.x, self.y)
        lower_right_corner = (self.x + self.w, self.y)
        upper_right_corner = (self.x + self.w, self.y + self.d)
        upper_left_corner = (self.x, self.y + self.d)
        bottom_plane = [
            lower_left_corner,
            lower_right_corner,
            upper_right_corner,
            upper_left_corner,
        ]
        idf.add_block(
            name="shoebox",
            coordinates=bottom_plane,
            height=self.zones_height
            + (self.h if self.basement and self.zoning == "core/perim" else 0),
            num_stories=self.num_stories + self.basement_storey_count,
            zoning=self.zoning,
            perim_depth=self.perim_depth,
            below_ground_stories=self.basement_storey_count,
            below_ground_storey_height=self.h,
        )
        if self.basement and self.zoning == "core/perim":
            idf.translate((0, 0, -self.h))

        if self.roof_height:
            # we need to convert the old roof surfaces to ceilings;
            # additionally, we will track them so that we can create the
            # corresponding floor surfaces for the attic in a manner
            # that avoids having to subdivide surfaces with intersect/match
            old_roof_srfs = []
            for srf in idf.idfobjects["BUILDINGSURFACE:DETAILED"]:
                if srf.Surface_Type.lower() == "roof":
                    srf.Surface_Type = "ceiling"
                    old_roof_srfs.append(srf)
            if len(old_roof_srfs) not in [1, 5]:
                msg = "Too many roof surfaces were found; expected 1 (by_storey) or 5 "
                f" (core/perim), but found {len(old_roof_srfs)}."
                raise ValueError(msg)

            # create the zone
            idf.newidfobject("ZONE", Name="Attic")

            # we always want the centerline of a gable to be paralle to the longer
            # edge
            centerline_parallel_to = "w" if self.w > self.d else "d"

            # the centerline is the midpoint of the shorter edge
            # since it is parallel to the longer edge
            roof_centerline = (
                (self.x + self.w / 2)
                if centerline_parallel_to == "d"
                else (self.y + self.d / 2)
            )

            if centerline_parallel_to == "d":
                # this gable goes from the left edge of the building to
                # the midpoint on the x-axis
                # it starts in the "upper left" corner in plan
                # and goes counter clockwise to the "lower left" corner
                # then to the roof centerline (and up in the z-axis)
                vert_0 = (self.x, self.y + self.d, self.zones_height)
                vert_1 = (self.x, self.y, self.zones_height)
                vert_2 = (roof_centerline, self.y, self.total_height_with_gabling)
                vert_3 = (
                    roof_centerline,
                    self.y + self.d,
                    self.total_height_with_gabling,
                )
            else:
                # this gable goes from the middle of the left edge at the top of the
                # gable and goes counter clockwise down to the lower left corner
                # then the lower right corner, and then back up.
                vert_0 = (self.x, roof_centerline, self.total_height_with_gabling)
                vert_1 = (self.x, self.y, self.zones_height)
                vert_2 = (self.x + self.w, self.y, self.zones_height)
                vert_3 = (
                    self.x + self.w,
                    roof_centerline,
                    self.total_height_with_gabling,
                )

            idf.newidfobject(
                "BUILDINGSURFACE:DETAILED",
                Name="Gable1",
                Surface_Type="Roof",
                Number_of_Vertices=4,
                View_Factor_to_Ground=0,
                Vertex_1_Xcoordinate=vert_0[0],
                Vertex_1_Ycoordinate=vert_0[1],
                Vertex_1_Zcoordinate=vert_0[2],
                Vertex_2_Xcoordinate=vert_1[0],
                Vertex_2_Ycoordinate=vert_1[1],
                Vertex_2_Zcoordinate=vert_1[2],
                Vertex_3_Xcoordinate=vert_2[0],
                Vertex_3_Ycoordinate=vert_2[1],
                Vertex_3_Zcoordinate=vert_2[2],
                Vertex_4_Xcoordinate=vert_3[0],
                Vertex_4_Ycoordinate=vert_3[1],
                Vertex_4_Zcoordinate=vert_3[2],
                Zone_Name="Attic",
            )

            if centerline_parallel_to == "d":
                vert_0 = (self.x + self.w, self.y, self.zones_height)
                vert_1 = (self.x + self.w, self.y + self.d, self.zones_height)
                vert_2 = (
                    roof_centerline,
                    self.y + self.d,
                    self.total_height_with_gabling,
                )
                vert_3 = (
                    roof_centerline,
                    self.y,
                    self.total_height_with_gabling,
                )
            else:
                vert_0 = (self.x, roof_centerline, self.total_height_with_gabling)
                vert_1 = (
                    self.x + self.w,
                    roof_centerline,
                    self.total_height_with_gabling,
                )
                vert_2 = (
                    self.x + self.w,
                    self.y + self.d,
                    self.zones_height,
                )
                vert_3 = (
                    self.x,
                    self.y + self.d,
                    self.zones_height,
                )

            idf.newidfobject(
                "BUILDINGSURFACE:DETAILED",
                Name="Gable2",
                Surface_Type="Roof",
                Number_of_Vertices=4,
                View_Factor_to_Ground=0,
                Vertex_1_Xcoordinate=vert_0[0],
                Vertex_1_Ycoordinate=vert_0[1],
                Vertex_1_Zcoordinate=vert_0[2],
                Vertex_2_Xcoordinate=vert_1[0],
                Vertex_2_Ycoordinate=vert_1[1],
                Vertex_2_Zcoordinate=vert_1[2],
                Vertex_3_Xcoordinate=vert_2[0],
                Vertex_3_Ycoordinate=vert_2[1],
                Vertex_3_Zcoordinate=vert_2[2],
                Vertex_4_Xcoordinate=vert_3[0],
                Vertex_4_Ycoordinate=vert_3[1],
                Vertex_4_Zcoordinate=vert_3[2],
                Zone_Name="Attic",
            )

            # make triangular endcaps
            if centerline_parallel_to == "d":
                vert_0 = (self.x, self.y, self.zones_height)
                vert_1 = (self.x + self.w, self.y, self.zones_height)
                vert_2 = (roof_centerline, self.y, self.total_height_with_gabling)
            else:
                vert_0 = (self.x, self.y, self.zones_height)
                vert_1 = (self.x, roof_centerline, self.total_height_with_gabling)
                vert_2 = (self.x, self.y + self.d, self.zones_height)

            idf.newidfobject(
                "BUILDINGSURFACE:DETAILED",
                Name="Endcap1",
                Surface_Type="Wall",
                Number_of_Vertices=3,
                Vertex_1_Xcoordinate=vert_0[0],
                Vertex_1_Ycoordinate=vert_0[1],
                Vertex_1_Zcoordinate=vert_0[2],
                Vertex_2_Xcoordinate=vert_1[0],
                Vertex_2_Ycoordinate=vert_1[1],
                Vertex_2_Zcoordinate=vert_1[2],
                Vertex_3_Xcoordinate=vert_2[0],
                Vertex_3_Ycoordinate=vert_2[1],
                Vertex_3_Zcoordinate=vert_2[2],
                Zone_Name="Attic",
            )

            if centerline_parallel_to == "d":
                vert_0 = (self.x + self.w, self.y + self.d, self.zones_height)
                vert_1 = (self.x, self.y + self.d, self.zones_height)
                vert_2 = (
                    roof_centerline,
                    self.y + self.d,
                    self.total_height_with_gabling,
                )
            else:
                vert_0 = (self.x + self.w, self.y, self.zones_height)
                vert_1 = (self.x + self.w, self.y + self.d, self.zones_height)
                vert_2 = (
                    self.x + self.w,
                    roof_centerline,
                    self.total_height_with_gabling,
                )

            idf.newidfobject(
                "BUILDINGSURFACE:DETAILED",
                Name="Endcap2",
                Surface_Type="Wall",
                Number_of_Vertices=3,
                Vertex_1_Xcoordinate=vert_0[0],
                Vertex_1_Ycoordinate=vert_0[1],
                Vertex_1_Zcoordinate=vert_0[2],
                Vertex_2_Xcoordinate=vert_1[0],
                Vertex_2_Ycoordinate=vert_1[1],
                Vertex_2_Zcoordinate=vert_1[2],
                Vertex_3_Xcoordinate=vert_2[0],
                Vertex_3_Ycoordinate=vert_2[1],
                Vertex_3_Zcoordinate=vert_2[2],
                Zone_Name="Attic",
            )

            # We will create identical floor surfaces for the attic to match
            # the zone below.  While we could just add a single plane and let
            # the `intersect_match` handle it, this is more robust; the geomeppy
            # method occasionally results in numerical floating point errors where
            # very small overhang area is created with an outside boundary
            # condition.
            # we use a vertex order of 1, 4, 3, 2 to match the orientation of the
            # roof surfaces below it, i.e. CCW vs CW.
            for i, srf in enumerate(old_roof_srfs):
                idf.newidfobject(
                    "BUILDINGSURFACE:DETAILED",
                    Name=f"attic_bottom_plane_{i}",
                    Surface_Type="Floor",
                    Number_of_Vertices=4,
                    Vertex_1_Xcoordinate=srf.Vertex_1_Xcoordinate,
                    Vertex_1_Ycoordinate=srf.Vertex_1_Ycoordinate,
                    Vertex_1_Zcoordinate=srf.Vertex_1_Zcoordinate,
                    Vertex_2_Xcoordinate=srf.Vertex_4_Xcoordinate,
                    Vertex_2_Ycoordinate=srf.Vertex_4_Ycoordinate,
                    Vertex_2_Zcoordinate=srf.Vertex_4_Zcoordinate,
                    Vertex_3_Xcoordinate=srf.Vertex_3_Xcoordinate,
                    Vertex_3_Ycoordinate=srf.Vertex_3_Ycoordinate,
                    Vertex_3_Zcoordinate=srf.Vertex_3_Zcoordinate,
                    Vertex_4_Xcoordinate=srf.Vertex_2_Xcoordinate,
                    Vertex_4_Ycoordinate=srf.Vertex_2_Ycoordinate,
                    Vertex_4_Zcoordinate=srf.Vertex_2_Zcoordinate,
                    Zone_Name="Attic",
                )

        idf.intersect_match()

        idf.set_default_constructions()

        # Handle Windows
        window_walls = [
            w
            for w in idf.idfobjects["BUILDINGSURFACE:DETAILED"]
            if w.Outside_Boundary_Condition.lower() == "outdoors"
            and "attic" not in w.Zone_Name.lower()
            and (
                not w.Zone_Name.lower().endswith(self.basement_suffix.lower())
                if self.basement
                else True
            )
            and w.Surface_Type.lower() == "wall"
        ]
        idf.set_wwr(
            wwr=self.wwr,
            construction="Project External Window",
            force=True,
            surfaces=window_walls,
        )
        return idf

attic_storey_count property #

Return the number of attic stories.

basement_storey_count property #

Return the number of basement stories.

basement_suffix property #

Return the basement suffix for the building.

footprint_area property #

Return the total floor area of the building.

total_area property #

Return the total area of the building.

total_height_with_gabling property #

Return the total height of the building, including any gabling.

total_living_area property #

Return the total living area of the building (does not include attic/basement).

zones_height property #

Return the total height of the zones, excluding any gabling.

zones_per_storey property #

Return the number of zones per storey.

add(idf) #

Constructs a simple shoebox geometry in the IDF model.

Takes advantage of the geomeppy methods to do so.

Can create gables, basements, and various zoning strategies.

Parameters:

Name Type Description Default
idf IDF

The IDF model to add the geometry to.

required

Returns:

Type Description
IDF

The IDF model with the added geometry.

Source code in epinterface/geometry.py
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
def add(self, idf: IDF) -> IDF:  # noqa: C901
    """Constructs a simple shoebox geometry in the IDF model.

    Takes advantage of the geomeppy methods to do so.

    Can create gables, basements, and various zoning strategies.

    Args:
        idf: The IDF model to add the geometry to.

    Returns:
        The IDF model with the added geometry.
    """
    lower_left_corner = (self.x, self.y)
    lower_right_corner = (self.x + self.w, self.y)
    upper_right_corner = (self.x + self.w, self.y + self.d)
    upper_left_corner = (self.x, self.y + self.d)
    bottom_plane = [
        lower_left_corner,
        lower_right_corner,
        upper_right_corner,
        upper_left_corner,
    ]
    idf.add_block(
        name="shoebox",
        coordinates=bottom_plane,
        height=self.zones_height
        + (self.h if self.basement and self.zoning == "core/perim" else 0),
        num_stories=self.num_stories + self.basement_storey_count,
        zoning=self.zoning,
        perim_depth=self.perim_depth,
        below_ground_stories=self.basement_storey_count,
        below_ground_storey_height=self.h,
    )
    if self.basement and self.zoning == "core/perim":
        idf.translate((0, 0, -self.h))

    if self.roof_height:
        # we need to convert the old roof surfaces to ceilings;
        # additionally, we will track them so that we can create the
        # corresponding floor surfaces for the attic in a manner
        # that avoids having to subdivide surfaces with intersect/match
        old_roof_srfs = []
        for srf in idf.idfobjects["BUILDINGSURFACE:DETAILED"]:
            if srf.Surface_Type.lower() == "roof":
                srf.Surface_Type = "ceiling"
                old_roof_srfs.append(srf)
        if len(old_roof_srfs) not in [1, 5]:
            msg = "Too many roof surfaces were found; expected 1 (by_storey) or 5 "
            f" (core/perim), but found {len(old_roof_srfs)}."
            raise ValueError(msg)

        # create the zone
        idf.newidfobject("ZONE", Name="Attic")

        # we always want the centerline of a gable to be paralle to the longer
        # edge
        centerline_parallel_to = "w" if self.w > self.d else "d"

        # the centerline is the midpoint of the shorter edge
        # since it is parallel to the longer edge
        roof_centerline = (
            (self.x + self.w / 2)
            if centerline_parallel_to == "d"
            else (self.y + self.d / 2)
        )

        if centerline_parallel_to == "d":
            # this gable goes from the left edge of the building to
            # the midpoint on the x-axis
            # it starts in the "upper left" corner in plan
            # and goes counter clockwise to the "lower left" corner
            # then to the roof centerline (and up in the z-axis)
            vert_0 = (self.x, self.y + self.d, self.zones_height)
            vert_1 = (self.x, self.y, self.zones_height)
            vert_2 = (roof_centerline, self.y, self.total_height_with_gabling)
            vert_3 = (
                roof_centerline,
                self.y + self.d,
                self.total_height_with_gabling,
            )
        else:
            # this gable goes from the middle of the left edge at the top of the
            # gable and goes counter clockwise down to the lower left corner
            # then the lower right corner, and then back up.
            vert_0 = (self.x, roof_centerline, self.total_height_with_gabling)
            vert_1 = (self.x, self.y, self.zones_height)
            vert_2 = (self.x + self.w, self.y, self.zones_height)
            vert_3 = (
                self.x + self.w,
                roof_centerline,
                self.total_height_with_gabling,
            )

        idf.newidfobject(
            "BUILDINGSURFACE:DETAILED",
            Name="Gable1",
            Surface_Type="Roof",
            Number_of_Vertices=4,
            View_Factor_to_Ground=0,
            Vertex_1_Xcoordinate=vert_0[0],
            Vertex_1_Ycoordinate=vert_0[1],
            Vertex_1_Zcoordinate=vert_0[2],
            Vertex_2_Xcoordinate=vert_1[0],
            Vertex_2_Ycoordinate=vert_1[1],
            Vertex_2_Zcoordinate=vert_1[2],
            Vertex_3_Xcoordinate=vert_2[0],
            Vertex_3_Ycoordinate=vert_2[1],
            Vertex_3_Zcoordinate=vert_2[2],
            Vertex_4_Xcoordinate=vert_3[0],
            Vertex_4_Ycoordinate=vert_3[1],
            Vertex_4_Zcoordinate=vert_3[2],
            Zone_Name="Attic",
        )

        if centerline_parallel_to == "d":
            vert_0 = (self.x + self.w, self.y, self.zones_height)
            vert_1 = (self.x + self.w, self.y + self.d, self.zones_height)
            vert_2 = (
                roof_centerline,
                self.y + self.d,
                self.total_height_with_gabling,
            )
            vert_3 = (
                roof_centerline,
                self.y,
                self.total_height_with_gabling,
            )
        else:
            vert_0 = (self.x, roof_centerline, self.total_height_with_gabling)
            vert_1 = (
                self.x + self.w,
                roof_centerline,
                self.total_height_with_gabling,
            )
            vert_2 = (
                self.x + self.w,
                self.y + self.d,
                self.zones_height,
            )
            vert_3 = (
                self.x,
                self.y + self.d,
                self.zones_height,
            )

        idf.newidfobject(
            "BUILDINGSURFACE:DETAILED",
            Name="Gable2",
            Surface_Type="Roof",
            Number_of_Vertices=4,
            View_Factor_to_Ground=0,
            Vertex_1_Xcoordinate=vert_0[0],
            Vertex_1_Ycoordinate=vert_0[1],
            Vertex_1_Zcoordinate=vert_0[2],
            Vertex_2_Xcoordinate=vert_1[0],
            Vertex_2_Ycoordinate=vert_1[1],
            Vertex_2_Zcoordinate=vert_1[2],
            Vertex_3_Xcoordinate=vert_2[0],
            Vertex_3_Ycoordinate=vert_2[1],
            Vertex_3_Zcoordinate=vert_2[2],
            Vertex_4_Xcoordinate=vert_3[0],
            Vertex_4_Ycoordinate=vert_3[1],
            Vertex_4_Zcoordinate=vert_3[2],
            Zone_Name="Attic",
        )

        # make triangular endcaps
        if centerline_parallel_to == "d":
            vert_0 = (self.x, self.y, self.zones_height)
            vert_1 = (self.x + self.w, self.y, self.zones_height)
            vert_2 = (roof_centerline, self.y, self.total_height_with_gabling)
        else:
            vert_0 = (self.x, self.y, self.zones_height)
            vert_1 = (self.x, roof_centerline, self.total_height_with_gabling)
            vert_2 = (self.x, self.y + self.d, self.zones_height)

        idf.newidfobject(
            "BUILDINGSURFACE:DETAILED",
            Name="Endcap1",
            Surface_Type="Wall",
            Number_of_Vertices=3,
            Vertex_1_Xcoordinate=vert_0[0],
            Vertex_1_Ycoordinate=vert_0[1],
            Vertex_1_Zcoordinate=vert_0[2],
            Vertex_2_Xcoordinate=vert_1[0],
            Vertex_2_Ycoordinate=vert_1[1],
            Vertex_2_Zcoordinate=vert_1[2],
            Vertex_3_Xcoordinate=vert_2[0],
            Vertex_3_Ycoordinate=vert_2[1],
            Vertex_3_Zcoordinate=vert_2[2],
            Zone_Name="Attic",
        )

        if centerline_parallel_to == "d":
            vert_0 = (self.x + self.w, self.y + self.d, self.zones_height)
            vert_1 = (self.x, self.y + self.d, self.zones_height)
            vert_2 = (
                roof_centerline,
                self.y + self.d,
                self.total_height_with_gabling,
            )
        else:
            vert_0 = (self.x + self.w, self.y, self.zones_height)
            vert_1 = (self.x + self.w, self.y + self.d, self.zones_height)
            vert_2 = (
                self.x + self.w,
                roof_centerline,
                self.total_height_with_gabling,
            )

        idf.newidfobject(
            "BUILDINGSURFACE:DETAILED",
            Name="Endcap2",
            Surface_Type="Wall",
            Number_of_Vertices=3,
            Vertex_1_Xcoordinate=vert_0[0],
            Vertex_1_Ycoordinate=vert_0[1],
            Vertex_1_Zcoordinate=vert_0[2],
            Vertex_2_Xcoordinate=vert_1[0],
            Vertex_2_Ycoordinate=vert_1[1],
            Vertex_2_Zcoordinate=vert_1[2],
            Vertex_3_Xcoordinate=vert_2[0],
            Vertex_3_Ycoordinate=vert_2[1],
            Vertex_3_Zcoordinate=vert_2[2],
            Zone_Name="Attic",
        )

        # We will create identical floor surfaces for the attic to match
        # the zone below.  While we could just add a single plane and let
        # the `intersect_match` handle it, this is more robust; the geomeppy
        # method occasionally results in numerical floating point errors where
        # very small overhang area is created with an outside boundary
        # condition.
        # we use a vertex order of 1, 4, 3, 2 to match the orientation of the
        # roof surfaces below it, i.e. CCW vs CW.
        for i, srf in enumerate(old_roof_srfs):
            idf.newidfobject(
                "BUILDINGSURFACE:DETAILED",
                Name=f"attic_bottom_plane_{i}",
                Surface_Type="Floor",
                Number_of_Vertices=4,
                Vertex_1_Xcoordinate=srf.Vertex_1_Xcoordinate,
                Vertex_1_Ycoordinate=srf.Vertex_1_Ycoordinate,
                Vertex_1_Zcoordinate=srf.Vertex_1_Zcoordinate,
                Vertex_2_Xcoordinate=srf.Vertex_4_Xcoordinate,
                Vertex_2_Ycoordinate=srf.Vertex_4_Ycoordinate,
                Vertex_2_Zcoordinate=srf.Vertex_4_Zcoordinate,
                Vertex_3_Xcoordinate=srf.Vertex_3_Xcoordinate,
                Vertex_3_Ycoordinate=srf.Vertex_3_Ycoordinate,
                Vertex_3_Zcoordinate=srf.Vertex_3_Zcoordinate,
                Vertex_4_Xcoordinate=srf.Vertex_2_Xcoordinate,
                Vertex_4_Ycoordinate=srf.Vertex_2_Ycoordinate,
                Vertex_4_Zcoordinate=srf.Vertex_2_Zcoordinate,
                Zone_Name="Attic",
            )

    idf.intersect_match()

    idf.set_default_constructions()

    # Handle Windows
    window_walls = [
        w
        for w in idf.idfobjects["BUILDINGSURFACE:DETAILED"]
        if w.Outside_Boundary_Condition.lower() == "outdoors"
        and "attic" not in w.Zone_Name.lower()
        and (
            not w.Zone_Name.lower().endswith(self.basement_suffix.lower())
            if self.basement
            else True
        )
        and w.Surface_Type.lower() == "wall"
    ]
    idf.set_wwr(
        wwr=self.wwr,
        construction="Project External Window",
        force=True,
        surfaces=window_walls,
    )
    return idf

compute_shading_mask(building, neighbors, neighbor_heights, azimuthal_angle) #

Compute the shading mask for the building.

This will emit a ray from the center of the building in every direction according to the azimuthal angle division of a circle.

It will compute the intersection of each ray with all the neighbor edges, and then determine the height of the each edge that intersects the ray.

That height is then used to determine an elevation angle; the max of the elevation angles for each ray is then the shading mask value for that direction.

Note that this checks all edges, so its crucial that the neighbors have already been culled to the relevant building to avoid unnecessary computation.

Parameters:

Name Type Description Default
building Polygon | str

The building to compute the shading mask for.

required
neighbors list[Polygon | str | None]

The neighbors to compute the shading mask for.

required
neighbor_heights list[float | int | None]

The heights of the neighbors.

required
azimuthal_angle float

The azimuthal angle to compute the shading mask for.

required

Returns:

Name Type Description
shading_mask ndarray

The shading mask for the building.

Source code in epinterface/geometry.py
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
def compute_shading_mask(
    building: Polygon | str,
    neighbors: Sequence[Polygon | str | None],
    neighbor_heights: Sequence[float | int | None],
    azimuthal_angle: float,
) -> np.ndarray:
    """Compute the shading mask for the building.

    This will emit a ray from the center of the building in
    every direction according to the azimuthal angle division
    of a circle.

    It will compute the intersection of each ray with all the neighbor edges,
    and then determine the height of the each edge that intersects the ray.

    That height is then used to determine an elevation angle; the max of the elevation
    angles for each ray is then the shading mask value for that direction.

    Note that this checks all edges, so its crucial that the neighbors have
    already been culled to the relevant building to avoid unnecessary computation.

    Args:
        building (Polygon | str): The building to compute the shading mask for.
        neighbors (list[Polygon | str | None]): The neighbors to compute the shading mask for.
        neighbor_heights (list[float | int | None]): The heights of the neighbors.
        azimuthal_angle (float): The azimuthal angle to compute the shading mask for.

    Returns:
        shading_mask (np.ndarray): The shading mask for the building.
    """
    building_geom = building if isinstance(building, Polygon) else from_wkt(building)

    neighbor_geo_and_height = [
        (cast(Polygon, from_wkt(n)), float(h)) if isinstance(n, str) else (n, float(h))
        for n, h in zip(neighbors, neighbor_heights, strict=True)
        if n is not None and h is not None
    ]
    safe_neighbor_geoms = [geom for geom, _ in neighbor_geo_and_height]
    safe_neighbor_heights = [height for _, height in neighbor_geo_and_height]

    # first we compute the number of rays we need to cast
    # along with the angles at which to cast them
    n_rays = int(2 * np.pi / azimuthal_angle)
    ray_angles = np.linspace(0, 2 * np.pi - azimuthal_angle, n_rays)
    ray_distance = 9999  # an arbitrarily large distance

    # extract the relevant geometry data
    centroid = building_geom.centroid

    shading_mask = np.zeros(n_rays)

    for ray_angle_idx, ray_angle in enumerate(ray_angles):
        # create the ray as a line segment
        # using basic trig
        x_off, y_off = (
            ray_distance * np.cos(ray_angle),
            ray_distance * np.sin(ray_angle),
        )
        centroid_moved = translate(centroid, x_off, y_off)
        ray = LineString([centroid, centroid_moved])

        # track the max elevation angle for this ray so far
        max_elevation_angle = 0

        for geom, height in zip(
            safe_neighbor_geoms, safe_neighbor_heights, strict=True
        ):
            # create the line segments of the boundary
            x_coords = np.array(geom.boundary.xy[0])
            y_coords = np.array(geom.boundary.xy[1])

            for x0, y0, x1, y1 in zip(
                x_coords[:-1],
                y_coords[:-1],
                x_coords[1:],
                y_coords[1:],
                strict=True,
            ):
                line = LineString([(x0, y0), (x1, y1)])

                # compute the intersection and continue
                # if there is no intersection
                intersection = ray.intersection(line)
                if intersection.is_empty:
                    continue

                # compute the elevation angle and store it if it
                # is greater than the current max
                distance = intersection.distance(centroid)
                elevation_angle = np.arctan2(height, distance)
                max_elevation_angle = max(max_elevation_angle, elevation_angle)

        shading_mask[ray_angle_idx] = max_elevation_angle
    return shading_mask

get_zone_floor_area(idf, zone_name) #

Get the floor area of a zone by iterating over building surfaces that are of type 'floor'.

If more than one floor is found, for now we will return an error; it could be possible in an attic where the floor below has perim/core zoning...

Parameters:

Name Type Description Default
idf IDF

The IDF model to get the floor area from.

required
zone_name str

The name of the zone to get the floor area from.

required

Returns:

Name Type Description
area float

The floor area of the zone [m2].

Source code in epinterface/geometry.py
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
def get_zone_floor_area(idf: IDF, zone_name: str) -> float:
    """Get the floor area of a zone by iterating over building surfaces that are of type 'floor'.

    If more than one floor is found, for now we will return an error; it could be possible in an
    attic where the floor below has perim/core zoning...

    Args:
        idf (IDF): The IDF model to get the floor area from.
        zone_name (str): The name of the zone to get the floor area from.

    Returns:
        area (float): The floor area of the zone [m2].
    """
    area = 0
    area_ct = 0
    for srf in idf.idfobjects["BUILDINGSURFACE:DETAILED"]:
        # TODO: ensure that this still works for basements and attics.
        if srf.Zone_Name == zone_name and srf.Surface_Type.lower() == "floor":
            poly = Polygon3D(srf.coords)
            if poly.area == 0:
                raise ValueError(f"INVALID_FLOOR:{zone_name}:{srf.Name}")
            area += float(poly.area)
            area_ct += 1
    if area_ct not in [1, 5]:
        raise ValueError(f"TOO_MANY_FLOORS:{zone_name}:{area_ct}")
    if area == 0 or area_ct == 0:
        raise ValueError(f"NO_AREA:{zone_name}")

    return area

get_zone_glazed_area(idf, zone_name) #

Calculate the total area of windows for a specific zone in the IDF model.

Parameters:

Name Type Description Default
idf IDF

The IDF model.

required
zone_name str

The name of the zone to calculate the window area for.

required

Returns:

Name Type Description
float float

The total area of windows in the specified zone.

Source code in epinterface/geometry.py
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
def get_zone_glazed_area(idf: IDF, zone_name: str) -> float:
    """Calculate the total area of windows for a specific zone in the IDF model.

    Args:
        idf (IDF): The IDF model.
        zone_name (str): The name of the zone to calculate the window area for.

    Returns:
        float: The total area of windows in the specified zone.
    """
    total_window_area = 0.0
    total_windows = 0

    for window in idf.idfobjects["FENESTRATIONSURFACE:DETAILED"]:
        parent_srf = idf.getobject(
            "BUILDINGSURFACE:DETAILED", window.Building_Surface_Name
        )
        if parent_srf is None:
            msg = f"BUILDINGSURFACE:DETAILED:{window.Building_Surface_Name} not found"
            raise ValueError(msg)
        if (
            parent_srf.Zone_Name.lower() == zone_name.lower()
            and window.Surface_Type.lower() == "window"
        ):
            poly = Polygon3D(window.coords)
            total_window_area += float(poly.area)
            total_windows += 1

    if total_windows not in [0, 1, 4]:
        msg = f"TOO_MANY_WINDOWS:{zone_name}:{total_windows}"
        raise ValueError(msg)

    return total_window_area

get_zone_glazed_area_alt(idf, zone_name) #

Calculate the total area of windows for a specific zone in the IDF model.

Parameters:

Name Type Description Default
idf IDF

The IDF model.

required
zone_name str

The name of the zone to calculate the window area for.

required

Returns:

Name Type Description
float float

The total area of windows in the specified zone.

Source code in epinterface/geometry.py
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
def get_zone_glazed_area_alt(idf: IDF, zone_name: str) -> float:
    """Calculate the total area of windows for a specific zone in the IDF model.

    Args:
        idf (IDF): The IDF model.
        zone_name (str): The name of the zone to calculate the window area for.

    Returns:
        float: The total area of windows in the specified zone.
    """
    total_window_area = 0.0
    total_windows = 0

    for window in idf.idfobjects["FENESTRATIONSURFACE:DETAILED"]:
        parent_srf = idf.getobject(
            "BUILDINGSURFACE:DETAILED", window.Building_Surface_Name
        )
        if parent_srf is None:
            msg = f"BUILDINGSURFACE:DETAILED:{window.Building_Surface_Name} not found"
            raise ValueError(msg)
        if (
            parent_srf.Zone_Name.lower() == zone_name.lower()
            and window.Surface_Type.lower() == "window"
        ):
            vertices = [
                (
                    window.Vertex_1_Xcoordinate,
                    window.Vertex_1_Ycoordinate,
                    window.Vertex_1_Zcoordinate,
                ),
                (
                    window.Vertex_2_Xcoordinate,
                    window.Vertex_2_Ycoordinate,
                    window.Vertex_2_Zcoordinate,
                ),
                (
                    window.Vertex_3_Xcoordinate,
                    window.Vertex_3_Ycoordinate,
                    window.Vertex_3_Zcoordinate,
                ),
                (
                    window.Vertex_4_Xcoordinate,
                    window.Vertex_4_Ycoordinate,
                    window.Vertex_4_Zcoordinate,
                ),
            ]
            # Assuming the window is a quadrilateral, calculate its area
            # This is a simplified calculation assuming the window is a rectangle
            width = (
                (vertices[1][0] - vertices[0][0]) ** 2
                + (vertices[1][1] - vertices[0][1]) ** 2
                + (vertices[1][2] - vertices[0][2]) ** 2
            ) ** 0.5
            height = (
                (vertices[2][0] - vertices[1][0]) ** 2
                + (vertices[2][1] - vertices[1][1]) ** 2
                + (vertices[2][2] - vertices[1][2]) ** 2
            ) ** 0.5
            area = width * height
            total_window_area += area
            total_windows += 1

    if total_windows not in [0, 1, 4]:
        msg = f"TOO_MANY_WINDOWS:{zone_name}:{total_windows}"
        raise ValueError(msg)

    alt_window_area = get_zone_glazed_area_alt(idf, zone_name)
    if not np.allclose(total_window_area, alt_window_area):
        msg = f"GLAZED_AREA_MISMATCH:{zone_name}:{total_window_area}:{alt_window_area}"
        raise ValueError(msg)
    return total_window_area

match_idf_to_building_and_neighbors(idf, building, neighbor_polys, neighbor_floors, neighbor_f2f_height, target_short_length, target_long_length, rotation_angle) #

Match an IDF model to a building and neighbors by scaling and rotating the IDF model and adding shading blocks for neighbors.

Parameters:

Name Type Description Default
idf IDF

The IDF model to match.

required
building Polygon | str

The building to match.

required
neighbor_polys list[Polygon | str | None]

The neighbors to inject as shading.

required
neighbor_floors list[float | int | None]

The counts of the neighbors.

required
neighbor_f2f_height float | None

The height of the building to match

required
target_short_length float

The target short length of the building.

required
target_long_length float

The target long length of the building.

required
rotation_angle float

The rotation angle of the building (radians).

required

Returns:

Name Type Description
idf IDF

The matched IDF model.

Source code in epinterface/geometry.py
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
def match_idf_to_building_and_neighbors(
    idf: IDF,
    building: Polygon | str,
    neighbor_polys: list[Polygon | str | None],
    neighbor_floors: list[float | int | None],
    neighbor_f2f_height: float,
    target_short_length: float,
    target_long_length: float,
    rotation_angle: float,
) -> IDF:
    """Match an IDF model to a building and neighbors by scaling and rotating the IDF model and adding shading blocks for neighbors.

    Args:
        idf (IDF): The IDF model to match.
        building (Polygon | str): The building to match.
        neighbor_polys (list[Polygon | str | None]): The neighbors to inject as shading.
        neighbor_floors (list[float | int | None]): The counts of the neighbors.
        neighbor_f2f_height (float | None): The height of the building to match
        target_short_length (float): The target short length of the building.
        target_long_length (float): The target long length of the building.
        rotation_angle (float): The rotation angle of the building (radians).

    Returns:
        idf (IDF): The matched IDF model.
    """
    building_geo = (
        cast(Polygon, from_wkt(building)) if isinstance(building, str) else building
    )
    neighbor_geos = [
        (cast(Polygon, from_wkt(n)), h * neighbor_f2f_height)
        if isinstance(n, str)
        else (n, h * neighbor_f2f_height)
        for n, h in zip(neighbor_polys, neighbor_floors, strict=True)
        if n is not None and h is not None
    ]
    centroid = building_geo.centroid
    translated_neighbors = [
        (translate(n, xoff=-centroid.x, yoff=-centroid.y), h) for n, h in neighbor_geos
    ]
    idf_lengths = {(e.p1 - e.p2).length for e in idf.bounding_box().edges}
    idf_x_coords = [e.p1.x for e in idf.bounding_box().edges]
    x_span = max(idf_x_coords) - min(idf_x_coords)
    idf_y_coords = [e.p1.y for e in idf.bounding_box().edges]
    y_span = max(idf_y_coords) - min(idf_y_coords)
    # TODO: better handling for boxes that aren't [(0,0),...]
    if x_span < y_span:
        raise NotImplementedError(
            "This function assumes that the long edge is the x-axis, which is not the case."
        )
    x_min = min(idf_x_coords)
    y_min = min(idf_y_coords)
    if abs(x_min) > 1e-3 or abs(y_min) > 1e-3:
        raise NotImplementedError(
            "This function assumes that the building has the lowerleft corner at the origin, which is not the case."
        )
    if len(idf_lengths) > 2:
        raise NotImplementedError(
            "The IDF model is not a rectangle, which is not yet supported."
        )

    long_length = max(idf_lengths)
    short_length = min(idf_lengths)

    idf.scale(target_long_length / long_length, anchor=Vector2D(0, 0), axes="x")
    idf.scale(target_short_length / short_length, anchor=Vector2D(0, 0), axes="y")
    idf.translate((
        -target_long_length / 2,
        -target_short_length / 2,
        0,
    ))  # This translation makes an assumption that the source building is at [(0,0),(0,w),...]
    idf.rotate(rotation_angle * 180 / np.pi)
    for i, (geom, height) in enumerate(translated_neighbors):
        if not height:
            height = 3.5 * 2
        if np.isnan(height):
            height = 3.5 * 2
        idf.add_shading_block(
            name=f"shading_{i}",
            coordinates=[Vector2D(*coord) for coord in geom.exterior.coords[:-1]],
            height=height,
        )
    return idf

prepare_neighbor_shading_for_idf(building, neighbors, neighbor_heights, *, azimuthal_angle=2 * np.pi / 48, fence_radius=100, outward_offset=2, f2f_height) #

Prepare neighbor polygons and floor counts for match_idf_to_building_and_neighbors.

Computes a shading mask from the building and neighbors, converts it to shading fence quadrilaterals, and returns polygons plus floor counts suitable for IDF shading blocks.

Parameters:

Name Type Description Default
building Polygon | str

The building polygon (or WKT string).

required
neighbors Sequence[Polygon | str | None]

Neighbor polygons (or WKT strings).

required
neighbor_heights Sequence[float | int | None]

Heights of each neighbor [m].

required
azimuthal_angle float

Angular spacing for shading rays (default 2π/48).

2 * pi / 48
fence_radius float

Radius for shading fence tangency points.

100
outward_offset float

Distance to extend fence quadrilaterals outward.

2
f2f_height float

Floor-to-floor height for converting heights to floor counts.

required

Returns:

Name Type Description
mask_polys list[Polygon]

List of Shapely Polygons (quadrilaterals) for each shading fence.

neighbor_floors list[int]

List of floor counts (int) for each fence.

Source code in epinterface/geometry.py
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
def prepare_neighbor_shading_for_idf(
    building: Polygon | str,
    neighbors: Sequence[Polygon | str | None],
    neighbor_heights: Sequence[float | int | None],
    *,
    azimuthal_angle: float = 2 * np.pi / 48,
    fence_radius: float = 100,
    outward_offset: float = 2,
    f2f_height: float,
) -> tuple[list[Polygon], list[int]]:
    """Prepare neighbor polygons and floor counts for match_idf_to_building_and_neighbors.

    Computes a shading mask from the building and neighbors, converts it to shading fence
    quadrilaterals, and returns polygons plus floor counts suitable for IDF shading blocks.

    Args:
        building: The building polygon (or WKT string).
        neighbors: Neighbor polygons (or WKT strings).
        neighbor_heights: Heights of each neighbor [m].
        azimuthal_angle: Angular spacing for shading rays (default 2π/48).
        fence_radius: Radius for shading fence tangency points.
        outward_offset: Distance to extend fence quadrilaterals outward.
        f2f_height: Floor-to-floor height for converting heights to floor counts.

    Returns:
        mask_polys: List of Shapely Polygons (quadrilaterals) for each shading fence.
        neighbor_floors: List of floor counts (int) for each fence.
    """
    shading_mask = compute_shading_mask(
        building, neighbors, neighbor_heights, azimuthal_angle
    )
    az, p0, p1, h, _w = shading_fence_closed_ring(
        elevations=shading_mask, d=fence_radius
    )

    building_geom = building if isinstance(building, Polygon) else from_wkt(building)
    centroid = building_geom.centroid
    cx, cy = centroid.x, centroid.y

    angles = 2 * np.pi * np.arange(len(az)) / len(az)
    outward = np.stack([np.cos(angles), np.sin(angles)], axis=-1)
    p2 = p1 + outward_offset * outward
    p3 = p0 + outward_offset * outward

    mask_polys = [
        Polygon([
            (p0[i, 0] + cx, p0[i, 1] + cy),
            (p1[i, 0] + cx, p1[i, 1] + cy),
            (p2[i, 0] + cx, p2[i, 1] + cy),
            (p3[i, 0] + cx, p3[i, 1] + cy),
            (p0[i, 0] + cx, p0[i, 1] + cy),
        ])
        for i in range(len(az))
    ]
    neighbor_floors = [int(h[i] // f2f_height) for i in range(len(h))]

    return mask_polys, neighbor_floors

shading_fence_closed_ring(elevations, d) #

Construct N vertical 'shading fence' rectangles whose bases are tangent segments forming a closed regular polygon around a circle of radius d.

Inputs

elevations: (N,) elevation angles theta_k [radians] d: radius to tangency points (base midpoints)

Outputs

azimuths: (N,) inferred azimuths alpha_k = 2πk/N p0: (N, 2) base endpoint A (x,y) p1: (N, 2) base endpoint B (x,y) h: (N,) heights h_k = d * tan(theta_k) w: scalar side length / segment width = 2 d tan(π/N)

Notes
  • With this construction, the segments intersect/meet: p1[k] == p0[k+1] (cyclic), up to floating point tolerance.
  • N must be >= 3 for a closed polygon.
Source code in epinterface/geometry.py
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
def shading_fence_closed_ring(
    elevations: ArrayLike,
    d: float,
) -> tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray, float]:
    """Construct N vertical 'shading fence' rectangles whose bases are tangent segments forming a closed regular polygon around a circle of radius d.

    Inputs:
      elevations: (N,) elevation angles theta_k [radians]
      d: radius to tangency points (base midpoints)

    Outputs:
      azimuths: (N,) inferred azimuths alpha_k = 2πk/N
      p0:       (N, 2) base endpoint A (x,y)
      p1:       (N, 2) base endpoint B (x,y)
      h:        (N,) heights h_k = d * tan(theta_k)
      w:        scalar side length / segment width = 2 d tan(π/N)

    Notes:
      - With this construction, the segments intersect/meet: p1[k] == p0[k+1] (cyclic),
        up to floating point tolerance.
      - N must be >= 3 for a closed polygon.
    """
    theta = np.asarray(elevations, dtype=np.float64)
    if theta.ndim != 1:
        msg = f"elevations must be 1D, got shape {theta.shape}"
        raise ValueError(msg)

    N = theta.shape[0]
    if N < 3:
        msg = "Need at least 3 elevations (N >= 3) to form a closed ring."
        raise ValueError(msg)

    # Inferred equally spaced azimuths
    k = np.arange(N, dtype=np.float64)
    azimuths = 2.0 * np.pi * k / N

    ca, sa = np.cos(azimuths), np.sin(azimuths)

    # Tangency points (base midpoints) on circle radius d
    px = d * ca
    py = d * sa

    # Unit tangent direction (perpendicular to radius)
    tx = -sa
    ty = ca

    # Choose width so adjacent tangent segments meet (circumscribed regular N-gon)
    half_w = d * np.tan(np.pi / N)
    w = 2.0 * half_w

    # Endpoints in xy: p ± half_w * t
    p0 = np.stack([px - half_w * tx, py - half_w * ty], axis=-1)
    p1 = np.stack([px + half_w * tx, py + half_w * ty], axis=-1)

    # Heights from elevation angles
    h = d * np.tan(theta)

    return azimuths, p0, p1, h, w