422 lines
18 KiB
C
422 lines
18 KiB
C
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/*
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==============================================================================
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This file is part of the JUCE library.
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Copyright (c) 2020 - Raw Material Software Limited
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JUCE is an open source library subject to commercial or open-source
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licensing.
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By using JUCE, you agree to the terms of both the JUCE 6 End-User License
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Agreement and JUCE Privacy Policy (both effective as of the 16th June 2020).
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End User License Agreement: www.juce.com/juce-6-licence
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Privacy Policy: www.juce.com/juce-privacy-policy
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Or: You may also use this code under the terms of the GPL v3 (see
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www.gnu.org/licenses).
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JUCE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL WARRANTIES, WHETHER
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EXPRESSED OR IMPLIED, INCLUDING MERCHANTABILITY AND FITNESS FOR PURPOSE, ARE
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DISCLAIMED.
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==============================================================================
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*/
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namespace juce
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{
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//==============================================================================
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/**
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Represents a line.
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This class contains a bunch of useful methods for various geometric
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tasks.
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The ValueType template parameter should be a primitive type - float or double
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are what it's designed for. Integer types will work in a basic way, but some methods
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that perform mathematical operations may not compile, or they may not produce
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sensible results.
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@see Point, Rectangle, Path, Graphics::drawLine
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@tags{Graphics}
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*/
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template <typename ValueType>
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class Line
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{
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public:
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//==============================================================================
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/** Creates a line, using (0, 0) as its start and end points. */
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Line() = default;
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/** Creates a copy of another line. */
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Line (const Line&) = default;
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/** Creates a line based on the coordinates of its start and end points. */
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Line (ValueType startX, ValueType startY, ValueType endX, ValueType endY) noexcept
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: start (startX, startY), end (endX, endY)
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{
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}
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/** Creates a line from its start and end points. */
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Line (Point<ValueType> startPoint, Point<ValueType> endPoint) noexcept
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: start (startPoint), end (endPoint)
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{
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}
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/** Copies a line from another one. */
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Line& operator= (const Line&) = default;
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/** Destructor. */
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~Line() = default;
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//==============================================================================
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/** Returns the x coordinate of the line's start point. */
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inline ValueType getStartX() const noexcept { return start.x; }
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/** Returns the y coordinate of the line's start point. */
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inline ValueType getStartY() const noexcept { return start.y; }
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/** Returns the x coordinate of the line's end point. */
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inline ValueType getEndX() const noexcept { return end.x; }
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/** Returns the y coordinate of the line's end point. */
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inline ValueType getEndY() const noexcept { return end.y; }
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/** Returns the line's start point. */
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inline Point<ValueType> getStart() const noexcept { return start; }
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/** Returns the line's end point. */
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inline Point<ValueType> getEnd() const noexcept { return end; }
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/** Changes this line's start point */
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void setStart (ValueType newStartX, ValueType newStartY) noexcept { start.setXY (newStartX, newStartY); }
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/** Changes this line's end point */
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void setEnd (ValueType newEndX, ValueType newEndY) noexcept { end.setXY (newEndX, newEndY); }
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/** Changes this line's start point */
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void setStart (const Point<ValueType> newStart) noexcept { start = newStart; }
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/** Changes this line's end point */
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void setEnd (const Point<ValueType> newEnd) noexcept { end = newEnd; }
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/** Returns a line that is the same as this one, but with the start and end reversed, */
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Line reversed() const noexcept { return { end, start }; }
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/** Applies an affine transform to the line's start and end points. */
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void applyTransform (const AffineTransform& transform) noexcept
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{
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start.applyTransform (transform);
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end.applyTransform (transform);
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}
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//==============================================================================
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/** Returns the length of the line. */
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ValueType getLength() const noexcept { return start.getDistanceFrom (end); }
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/** Returns the length of the line. */
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ValueType getLengthSquared() const noexcept { return start.getDistanceSquaredFrom (end); }
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/** Returns true if the line's start and end x coordinates are the same. */
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bool isVertical() const noexcept { return start.x == end.x; }
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/** Returns true if the line's start and end y coordinates are the same. */
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bool isHorizontal() const noexcept { return start.y == end.y; }
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/** Returns the line's angle.
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This value is the number of radians clockwise from the 12 o'clock direction,
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where the line's start point is considered to be at the centre.
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*/
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typename Point<ValueType>::FloatType getAngle() const noexcept { return start.getAngleToPoint (end); }
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/** Creates a line from a start point, length and angle.
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This angle is the number of radians clockwise from the 12 o'clock direction,
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where the line's start point is considered to be at the centre.
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*/
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static Line fromStartAndAngle (Point<ValueType> startPoint, ValueType length, ValueType angle) noexcept
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{
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return { startPoint, startPoint.getPointOnCircumference (length, angle) };
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}
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//==============================================================================
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/** Casts this line to float coordinates. */
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Line<float> toFloat() const noexcept { return { start.toFloat(), end.toFloat() }; }
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/** Casts this line to double coordinates. */
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Line<double> toDouble() const noexcept { return { start.toDouble(), end.toDouble() }; }
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//==============================================================================
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/** Compares two lines. */
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bool operator== (Line other) const noexcept { return start == other.start && end == other.end; }
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/** Compares two lines. */
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bool operator!= (Line other) const noexcept { return start != other.start || end != other.end; }
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//==============================================================================
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/** Finds the intersection between two lines.
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@param line the line to intersect with
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@returns the point at which the lines intersect, even if this lies beyond the end of the lines
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*/
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Point<ValueType> getIntersection (Line line) const noexcept
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{
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Point<ValueType> p;
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findIntersection (start, end, line.start, line.end, p);
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return p;
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}
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/** Finds the intersection between two lines.
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@param line the other line
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@param intersection the position of the point where the lines meet (or
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where they would meet if they were infinitely long)
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the intersection (if the lines intersect). If the lines
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are parallel, this will just be set to the position
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of one of the line's endpoints.
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@returns true if the line segments intersect; false if they don't. Even if they
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don't intersect, the intersection coordinates returned will still
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be valid
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*/
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bool intersects (Line line, Point<ValueType>& intersection) const noexcept
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{
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return findIntersection (start, end, line.start, line.end, intersection);
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}
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/** Returns true if this line intersects another. */
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bool intersects (Line other) const noexcept
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{
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Point<ValueType> ignored;
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return findIntersection (start, end, other.start, other.end, ignored);
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}
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//==============================================================================
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/** Returns the location of the point which is a given distance along this line.
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@param distanceFromStart the distance to move along the line from its
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start point. This value can be negative or longer
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than the line itself
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@see getPointAlongLineProportionally
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*/
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Point<ValueType> getPointAlongLine (ValueType distanceFromStart) const noexcept
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{
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return start + (end - start) * (distanceFromStart / getLength());
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}
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/** Returns a point which is a certain distance along and to the side of this line.
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This effectively moves a given distance along the line, then another distance
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perpendicularly to this, and returns the resulting position.
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@param distanceFromStart the distance to move along the line from its
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start point. This value can be negative or longer
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than the line itself
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@param perpendicularDistance how far to move sideways from the line. If you're
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looking along the line from its start towards its
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end, then a positive value here will move to the
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right, negative value move to the left.
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*/
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Point<ValueType> getPointAlongLine (ValueType distanceFromStart,
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ValueType perpendicularDistance) const noexcept
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{
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auto delta = end - start;
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auto length = juce_hypot ((double) delta.x,
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(double) delta.y);
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if (length <= 0)
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return start;
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return { start.x + static_cast<ValueType> ((delta.x * distanceFromStart - delta.y * perpendicularDistance) / length),
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start.y + static_cast<ValueType> ((delta.y * distanceFromStart + delta.x * perpendicularDistance) / length) };
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}
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/** Returns the location of the point which is a given distance along this line
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proportional to the line's length.
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@param proportionOfLength the distance to move along the line from its
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start point, in multiples of the line's length.
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So a value of 0.0 will return the line's start point
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and a value of 1.0 will return its end point. (This value
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can be negative or greater than 1.0).
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@see getPointAlongLine
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*/
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Point<ValueType> getPointAlongLineProportionally (typename Point<ValueType>::FloatType proportionOfLength) const noexcept
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{
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return start + (end - start) * proportionOfLength;
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}
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/** Returns the smallest distance between this line segment and a given point.
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So if the point is close to the line, this will return the perpendicular
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distance from the line; if the point is a long way beyond one of the line's
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end-point's, it'll return the straight-line distance to the nearest end-point.
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pointOnLine receives the position of the point that is found.
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@returns the point's distance from the line
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@see getPositionAlongLineOfNearestPoint
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*/
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ValueType getDistanceFromPoint (Point<ValueType> targetPoint,
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Point<ValueType>& pointOnLine) const noexcept
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{
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auto delta = end - start;
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auto length = delta.x * delta.x + delta.y * delta.y;
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if (length > 0)
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{
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auto prop = ((targetPoint.x - start.x) * delta.x
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+ (targetPoint.y - start.y) * delta.y) / (double) length;
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if (prop >= 0 && prop <= 1.0)
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{
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pointOnLine = start + delta * prop;
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return targetPoint.getDistanceFrom (pointOnLine);
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}
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}
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auto fromStart = targetPoint.getDistanceFrom (start);
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auto fromEnd = targetPoint.getDistanceFrom (end);
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if (fromStart < fromEnd)
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{
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pointOnLine = start;
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return fromStart;
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}
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pointOnLine = end;
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return fromEnd;
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}
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/** Finds the point on this line which is nearest to a given point, and
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returns its position as a proportional position along the line.
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@returns a value 0 to 1.0 which is the distance along this line from the
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line's start to the point which is nearest to the point passed-in. To
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turn this number into a position, use getPointAlongLineProportionally().
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@see getDistanceFromPoint, getPointAlongLineProportionally
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*/
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ValueType findNearestProportionalPositionTo (Point<ValueType> point) const noexcept
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{
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auto delta = end - start;
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auto length = delta.x * delta.x + delta.y * delta.y;
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return length <= 0 ? 0
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: jlimit (ValueType(), static_cast<ValueType> (1),
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static_cast<ValueType> ((((point.x - start.x) * delta.x
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+ (point.y - start.y) * delta.y) / length)));
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}
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/** Finds the point on this line which is nearest to a given point.
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@see getDistanceFromPoint, findNearestProportionalPositionTo
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*/
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Point<ValueType> findNearestPointTo (Point<ValueType> point) const noexcept
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{
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return getPointAlongLineProportionally (findNearestProportionalPositionTo (point));
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}
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/** Returns true if the given point lies above this line.
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The return value is true if the point's y coordinate is less than the y
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coordinate of this line at the given x (assuming the line extends infinitely
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in both directions).
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*/
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bool isPointAbove (Point<ValueType> point) const noexcept
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{
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return start.x != end.x
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&& point.y < ((end.y - start.y) * (point.x - start.x)) / (end.x - start.x) + start.y;
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}
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//==============================================================================
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/** Returns a shortened copy of this line.
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This will chop off part of the start of this line by a certain amount, (leaving the
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end-point the same), and return the new line.
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*/
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Line withShortenedStart (ValueType distanceToShortenBy) const noexcept
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{
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return { getPointAlongLine (jmin (distanceToShortenBy, getLength())), end };
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}
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/** Returns a shortened copy of this line.
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This will chop off part of the end of this line by a certain amount, (leaving the
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start-point the same), and return the new line.
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*/
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Line withShortenedEnd (ValueType distanceToShortenBy) const noexcept
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{
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auto length = getLength();
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return { start, getPointAlongLine (length - jmin (distanceToShortenBy, length)) };
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}
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private:
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//==============================================================================
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Point<ValueType> start, end;
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static bool isZeroToOne (ValueType v) noexcept { return v >= 0 && v <= static_cast<ValueType> (1); }
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static bool findIntersection (const Point<ValueType> p1, const Point<ValueType> p2,
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const Point<ValueType> p3, const Point<ValueType> p4,
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Point<ValueType>& intersection) noexcept
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{
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if (p2 == p3)
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{
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intersection = p2;
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return true;
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}
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auto d1 = p2 - p1;
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auto d2 = p4 - p3;
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auto divisor = d1.x * d2.y - d2.x * d1.y;
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if (divisor == 0)
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{
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if (! (d1.isOrigin() || d2.isOrigin()))
|
||
|
|
{
|
||
|
|
if (d1.y == 0 && d2.y != 0)
|
||
|
|
{
|
||
|
|
auto along = (p1.y - p3.y) / d2.y;
|
||
|
|
intersection = p1.withX (p3.x + along * d2.x);
|
||
|
|
return isZeroToOne (along);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (d2.y == 0 && d1.y != 0)
|
||
|
|
{
|
||
|
|
auto along = (p3.y - p1.y) / d1.y;
|
||
|
|
intersection = p3.withX (p1.x + along * d1.x);
|
||
|
|
return isZeroToOne (along);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (d1.x == 0 && d2.x != 0)
|
||
|
|
{
|
||
|
|
auto along = (p1.x - p3.x) / d2.x;
|
||
|
|
intersection = p1.withY (p3.y + along * d2.y);
|
||
|
|
return isZeroToOne (along);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (d2.x == 0 && d1.x != 0)
|
||
|
|
{
|
||
|
|
auto along = (p3.x - p1.x) / d1.x;
|
||
|
|
intersection = p3.withY (p1.y + along * d1.y);
|
||
|
|
return isZeroToOne (along);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
intersection = (p2 + p3) / static_cast<ValueType> (2);
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
auto along1 = ((p1.y - p3.y) * d2.x - (p1.x - p3.x) * d2.y) / divisor;
|
||
|
|
intersection = p1 + d1 * along1;
|
||
|
|
|
||
|
|
if (! isZeroToOne (along1))
|
||
|
|
return false;
|
||
|
|
|
||
|
|
auto along2 = ((p1.y - p3.y) * d1.x - (p1.x - p3.x) * d1.y) / divisor;
|
||
|
|
return isZeroToOne (along2);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
} // namespace juce
|