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| Original file line number | Diff line number | Diff line change |
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| @@ -1,3 +1,7 @@ | ||
| ## [2.0.3] | ||
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| * Fix GMST calculations. | ||
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| ## [2.0.2] | ||
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| * Adds ground track (Footprint) calculations. | ||
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,209 @@ | ||
| part of '../latlng.dart'; | ||
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| /// Represents a 2D point on screen-space in pixels. | ||
| class Point2D { | ||
| const Point2D(this.x, this.y); | ||
| final double x; | ||
| final double y; | ||
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| /// Offsets a line by given [amount] in pixels. | ||
| List<Point2D> offset(List<Point2D> points, double amount) { | ||
| final offsetSegments = _offsetPointLine(points, amount); | ||
| return _joinLineSegments(offsetSegments, amount); | ||
| } | ||
| } | ||
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| void _forEachPair<T>(List<T> list, Function(T a, T b) callback) { | ||
| if (list.isEmpty) { | ||
| return; | ||
| } | ||
| for (var i = 1, l = list.length; i < l; i++) { | ||
| callback(list[i - 1], list[i]); | ||
| } | ||
| } | ||
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| /// Find the coefficients (a,b) of a line of equation y = a.x + b, | ||
| /// or the constant x for vertical lines | ||
| /// Return null if there's no equation possible | ||
| class _LineEquation { | ||
| const _LineEquation({this.x, this.a, this.b}); | ||
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| final double? x; | ||
| final double? a; | ||
| final double? b; | ||
| } | ||
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| class _OffsetSegment { | ||
| const _OffsetSegment({ | ||
| required this.offsetAngle, | ||
| required this.original, | ||
| required this.offset, | ||
| }); | ||
| final double offsetAngle; | ||
| final List<Point2D> original; | ||
| final List<Point2D> offset; | ||
| } | ||
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| _LineEquation? _lineEquation(Point2D pt1, Point2D pt2) { | ||
| if (pt1.x == pt2.x) { | ||
| return pt1.y == pt2.y ? null : _LineEquation(x: pt1.x); | ||
| } | ||
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| var a = (pt2.y - pt1.y) / (pt2.x - pt1.x); | ||
| return _LineEquation( | ||
| a: a, | ||
| b: pt1.y - a * pt1.x, | ||
| ); | ||
| } | ||
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| /// Return the intersection point of two lines defined by two points each | ||
| /// Return null when there's no unique intersection | ||
| Point2D? _intersection(Point2D l1a, Point2D l1b, Point2D l2a, Point2D l2b) { | ||
| var line1 = _lineEquation(l1a, l1b); | ||
| var line2 = _lineEquation(l2a, l2b); | ||
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| if (line1 == null || line2 == null) { | ||
| return null; | ||
| } | ||
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| if (line1.x != null) { | ||
| return line2.x != null | ||
| ? null | ||
| : Point2D( | ||
| line1.x!, | ||
| line2.a! * line1.x! + line2.b!, | ||
| ); | ||
| } | ||
| if (line2.x != null) { | ||
| return Point2D( | ||
| line2.x!, | ||
| line1.a! * line2.x! + line1.b!, | ||
| ); | ||
| } | ||
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| if (line1.a == line2.a) { | ||
| return null; | ||
| } | ||
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| var x = (line2.b! - line1.b!) / (line1.a! - line2.a!); | ||
| return Point2D( | ||
| x, | ||
| line1.a! * x + line1.b!, | ||
| ); | ||
| } | ||
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| Point2D _translatePoint(Point2D pt, double dist, double heading) { | ||
| return Point2D( | ||
| pt.x + dist * cos(heading), | ||
| pt.y + dist * sin(heading), | ||
| ); | ||
| } | ||
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| List<_OffsetSegment> _offsetPointLine(List<Point2D> points, double distance) { | ||
| var offsetSegments = <_OffsetSegment>[]; | ||
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| _forEachPair<Point2D>(points, (a, b) { | ||
| if (a.x == b.x && a.y == b.y) { | ||
| return; | ||
| } | ||
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| // angles in (-PI, PI] | ||
| var segmentAngle = atan2(a.y - b.y, a.x - b.x); | ||
| var offsetAngle = segmentAngle - pi / 2; | ||
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| offsetSegments.add(_OffsetSegment(offsetAngle: offsetAngle, original: [ | ||
| a, | ||
| b | ||
| ], offset: [ | ||
| _translatePoint(a, distance, offsetAngle), | ||
| _translatePoint(b, distance, offsetAngle) | ||
| ])); | ||
| }); | ||
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| return offsetSegments; | ||
| } | ||
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| /// Join 2 line segments defined by 2 points each with a circular arc | ||
| List<Point2D> _joinSegments( | ||
| _OffsetSegment s1, | ||
| _OffsetSegment s2, | ||
| double offset, | ||
| ) { | ||
| // TO DO: different join styles | ||
| return _circularArc(s1, s2, offset) | ||
| .where((x) { | ||
| return x != null; | ||
| }) | ||
| .map((e) => e!) | ||
| .toList(); | ||
| } | ||
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| List<Point2D> _joinLineSegments(List<_OffsetSegment> segments, double offset) { | ||
| var joinedPoints = <Point2D>[]; | ||
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| if (segments.isNotEmpty) { | ||
| var first = segments.first; | ||
| var last = segments.last; | ||
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| joinedPoints.add(first.offset[0]); | ||
| _forEachPair<_OffsetSegment>(segments, (s1, s2) { | ||
| joinedPoints = [...joinedPoints, ..._joinSegments(s1, s2, offset)]; | ||
| }); | ||
| joinedPoints.add(last.offset[1]); | ||
| } | ||
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| return joinedPoints; | ||
| } | ||
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| Point2D _segmentAsVector(List<Point2D> s) { | ||
| return Point2D( | ||
| s[1].x - s[0].x, | ||
| s[1].y - s[0].y, | ||
| ); | ||
| } | ||
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| double _getSignedAngle(List<Point2D> s1, List<Point2D> s2) { | ||
| final a = _segmentAsVector(s1); | ||
| final b = _segmentAsVector(s2); | ||
| return atan2(a.x * b.y - a.y * b.x, a.x * b.x + a.y * b.y); | ||
| } | ||
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| /// Interpolates points between two offset segments in a circular form | ||
| List<Point2D?> _circularArc( | ||
| _OffsetSegment s1, _OffsetSegment s2, double distance) { | ||
| // if the segments are the same angle, | ||
| // there should be a single join point | ||
| if (s1.offsetAngle == s2.offsetAngle) { | ||
| return [s1.offset[1]]; | ||
| } | ||
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| final signedAngle = _getSignedAngle(s1.offset, s2.offset); | ||
| // for inner angles, just find the offset segments intersection | ||
| if ((signedAngle * distance > 0) && | ||
| (signedAngle * _getSignedAngle(s1.offset, [s1.offset[0], s2.offset[1]]) > | ||
| 0)) { | ||
| return [ | ||
| _intersection(s1.offset[0], s1.offset[1], s2.offset[0], s2.offset[1]) | ||
| ]; | ||
| } | ||
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| // draws a circular arc with R = offset distance, C = original meeting point | ||
| var points = <Point2D>[]; | ||
| var center = s1.original[1]; | ||
| // ensure angles go in the anti-clockwise direction | ||
| var rightOffset = distance > 0; | ||
| var startAngle = rightOffset ? s2.offsetAngle : s1.offsetAngle; | ||
| var endAngle = rightOffset ? s1.offsetAngle : s2.offsetAngle; | ||
| // and that the end angle is bigger than the start angle | ||
| if (endAngle < startAngle) { | ||
| endAngle += pi * 2; | ||
| } | ||
| var step = pi / 8; | ||
| for (var alpha = startAngle; alpha < endAngle; alpha += step) { | ||
| points.add(_translatePoint(center, distance, alpha)); | ||
| } | ||
| points.add(_translatePoint(center, distance, endAngle)); | ||
|
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| return rightOffset ? points.reversed.toList() : points; | ||
| } |
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