envyen
6/30/2016 - 6:05 AM
Collection of methods to achieve better circular arc drawing, as Canvas.drawArc() is unreliable. See the related article: https://medium.com
Collection of methods to achieve better circular arc drawing, as Canvas.drawArc() is unreliable. See the related article: https://medium.com/p/9155f49166b8
/**
* ArcUtils.java
*
* Copyright (c) 2014 BioWink GmbH.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
**/
package com.biowink.clue;
import android.graphics.Canvas;
import android.graphics.Paint;
import android.graphics.Path;
import android.graphics.PointF;
import org.jetbrains.annotations.NotNull;
import org.jetbrains.annotations.Nullable;
import static java.lang.Math.abs;
import static java.lang.Math.ceil;
import static java.lang.Math.cos;
import static java.lang.Math.floor;
import static java.lang.Math.sin;
import static java.lang.Math.sqrt;
import static java.lang.Math.toRadians;
/**
* Collection of methods to achieve better circular arc drawing, as
* {@link Canvas#drawArc(android.graphics.RectF, float, float, boolean, android.graphics.Paint)} is unreliable.
* <p>
* To draw a simple arc, use
* {@link #drawArc(android.graphics.Canvas, android.graphics.PointF, float, float, float, android.graphics.Paint)}.
* </p>
*/
public final class ArcUtils
{
private static final double FULL_CIRCLE_RADIANS = toRadians(360d);
private ArcUtils() { }
/**
* Draws a circular arc on the given {@code Canvas}.
*
* @param canvas The canvas to draw into.
* @param circleCenter The center of the circle on which to draw the arc.
* @param circleRadius The radius of the circle on which to draw the arc.
* @param startAngle Starting angle (in degrees) where the arc begins.
* @param sweepAngle Sweep angle (in degrees) measured clockwise.
* @param paint The paint to use then drawing the arc.
*
* @see #drawArc(android.graphics.Canvas, android.graphics.PointF, float, float, float, android.graphics.Paint, int, boolean)
*/
public static void drawArc(@NotNull Canvas canvas, PointF circleCenter, float circleRadius,
float startAngle, float sweepAngle, @NotNull Paint paint)
{
drawArc(canvas, circleCenter, circleRadius, startAngle, sweepAngle, paint, 8, false);
}
/**
* Draws a circular arc on the given {@code Canvas}.
*
* @param canvas The canvas to draw into.
* @param circleCenter The center of the circle on which to draw the arc.
* @param circleRadius The radius of the circle on which to draw the arc.
* @param startAngle Starting angle (in degrees) where the arc begins.
* @param sweepAngle Sweep angle (in degrees) measured clockwise.
* @param paint The paint to use then drawing the arc.
* @param arcsPointsOnCircle See {@link #createBezierArcDegrees(android.graphics.PointF, float, float, float, int, boolean, android.graphics.Path)}.
* @param arcsOverlayPoints See {@link #createBezierArcDegrees(android.graphics.PointF, float, float, float, int, boolean, android.graphics.Path)}.
*
* @see #drawArc(android.graphics.Canvas, android.graphics.PointF, float, float, float, android.graphics.Paint)
*/
public static void drawArc(@NotNull Canvas canvas, PointF circleCenter, float circleRadius,
float startAngle, float sweepAngle, @NotNull Paint paint,
int arcsPointsOnCircle, boolean arcsOverlayPoints)
{
if (sweepAngle == 0f)
{
final PointF p = pointFromAngleDegrees(circleCenter, circleRadius, startAngle);
canvas.drawPoint(p.x, p.y, paint);
}
else
{
canvas.drawPath(createBezierArcDegrees(
circleCenter, circleRadius, startAngle, sweepAngle,
arcsPointsOnCircle, arcsOverlayPoints, null), paint);
}
}
/**
* Normalize the input radians in the range 360° > x >= 0°.
*
* @param radians The angle to normalize (in radians).
*
* @return The angle normalized in the range 360° > x >= 0°.
*/
public static double normalizeRadians(double radians)
{
radians %= FULL_CIRCLE_RADIANS;
if (radians < 0d) { radians += FULL_CIRCLE_RADIANS; }
if (radians == FULL_CIRCLE_RADIANS) { radians = 0d; }
return radians;
}
/**
* Returns the point of a given angle (in radians) on a circle.
*
* @param center The center of the circle.
* @param radius The radius of the circle.
* @param angleRadians The angle (in radians).
*
* @return The point of the given angle on the specified circle.
*
* @see #pointFromAngleDegrees(android.graphics.PointF, float, float)
*/
@NotNull
public static PointF pointFromAngleRadians(@NotNull PointF center, float radius, double angleRadians)
{
return new PointF((float)(center.x + radius * cos(angleRadians)),
(float)(center.y + radius * sin(angleRadians)));
}
/**
* Returns the point of a given angle (in degrees) on a circle.
*
* @param center The center of the circle.
* @param radius The radius of the circle.
* @param angleDegrees The angle (in degrees).
*
* @return The point of the given angle on the specified circle.
*
* @see #pointFromAngleRadians(android.graphics.PointF, float, double)
*/
@NotNull
public static PointF pointFromAngleDegrees(@NotNull PointF center, float radius, float angleDegrees)
{
return pointFromAngleRadians(center, radius, toRadians(angleDegrees));
}
/**
* Adds a circular arc to the given path by approximating it through a cubic Bézier curve.
* <p/>
* <p>
* Note that this <strong>does not</strong> split the arc to better approximate it, for that see either:
* <ul>
* <li>{@link #createBezierArcDegrees(android.graphics.PointF, float, float, float, int, boolean,
* android.graphics.Path)}</li>
* <li>{@link #createBezierArcRadians(android.graphics.PointF, float, double, double, int, boolean,
* android.graphics.Path)}</li>
* </ul>
* </p>
* <p/>
* For a technical explanation:
* <a href="http://hansmuller-flex.blogspot.de/2011/10/more-about-approximating-circular-arcs.html">
* http://hansmuller-flex.blogspot.de/2011/10/more-about-approximating-circular-arcs.html
* </a>
*
* @param path The path to add the arc to.
* @param center The center of the circle.
* @param start The starting point of the arc on the circle.
* @param end The ending point of the arc on the circle.
* @param moveToStart If {@code true}, move to the starting point of the arc
* (see: {@link android.graphics.Path#moveTo(float, float)}).
*
* @see #createBezierArcDegrees(android.graphics.PointF, float, float, float, int, boolean, android.graphics.Path)
* @see #createBezierArcRadians(android.graphics.PointF, float, double, double, int, boolean, android.graphics.Path)
*/
public static void addBezierArcToPath(@NotNull Path path, @NotNull PointF center,
@NotNull PointF start, @NotNull PointF end, boolean moveToStart)
{
if (moveToStart) { path.moveTo(start.x, start.y); }
if (start.equals(end)) { return; }
final double ax = start.x - center.x;
final double ay = start.y - center.y;
final double bx = end.x - center.x;
final double by = end.y - center.y;
final double q1 = ax * ax + ay * ay;
final double q2 = q1 + ax * bx + ay * by;
final double k2 = 4d / 3d * (sqrt(2d * q1 * q2) - q2) / (ax * by - ay * bx);
final float x2 = (float)(center.x + ax - k2 * ay);
final float y2 = (float)(center.y + ay + k2 * ax);
final float x3 = (float)(center.x + bx + k2 * by);
final float y3 = (float)(center.y + by - k2 * bx);
path.cubicTo(x2, y2, x3, y3, end.x, end.y);
}
/**
* Adds a circular arc to the given path by approximating it through a cubic Bézier curve, splitting it if
* necessary. The precision of the approximation can be adjusted through {@code pointsOnCircle} and
* {@code overlapPoints} parameters.
* <p>
* <strong>Example:</strong> imagine an arc starting from 0° and sweeping 100° with a value of
* {@code pointsOnCircle} equal to 12 (threshold -> 360° / 12 = 30°):
* <ul>
* <li>if {@code overlapPoints} is {@code true}, it will be split as following:
* <ul>
* <li>from 0° to 30° (sweep 30°)</li>
* <li>from 30° to 60° (sweep 30°)</li>
* <li>from 60° to 90° (sweep 30°)</li>
* <li>from 90° to 100° (sweep 10°)</li>
* </ul>
* </li>
* <li>if {@code overlapPoints} is {@code false}, it will be split into 4 equal arcs:
* <ul>
* <li>from 0° to 25° (sweep 25°)</li>
* <li>from 25° to 50° (sweep 25°)</li>
* <li>from 50° to 75° (sweep 25°)</li>
* <li>from 75° to 100° (sweep 25°)</li>
* </ul>
* </li>
* </ul>
* </p>
* <p/>
* For a technical explanation:
* <a href="http://hansmuller-flex.blogspot.de/2011/10/more-about-approximating-circular-arcs.html">
* http://hansmuller-flex.blogspot.de/2011/10/more-about-approximating-circular-arcs.html
* </a>
*
* @param center The center of the circle.
* @param radius The radius of the circle.
* @param startAngleRadians The starting angle on the circle (in radians).
* @param sweepAngleRadians How long to make the total arc (in radians).
* @param pointsOnCircle Defines a <i>threshold</i> (360° /{@code pointsOnCircle}) to split the Bézier arc to
* better approximate a circular arc, depending also on the value of {@code overlapPoints}.
* The suggested number to have a reasonable approximation of a circle is at least 4 (90°).
* Less than 1 will be ignored (the arc will not be split).
* @param overlapPoints Given the <i>threshold</i> defined through {@code pointsOnCircle}:
* <ul>
* <li>if {@code true}, split the arc on every angle which is a multiple of the
* <i>threshold</i> (yields better results if drawing precision is required,
* especially when stacking multiple arcs, but can potentially use more points)</li>
* <li>if {@code false}, split the arc equally so that each part is shorter than
* the <i>threshold</i></li>
* </ul>
* @param addToPath An existing path where to add the arc to, or {@code null} to create a new path.
*
* @return {@code addToPath} if it's not {@code null}, otherwise a new path.
*
* @see #createBezierArcDegrees(android.graphics.PointF, float, float, float, int, boolean, android.graphics.Path)
*/
@NotNull
public static Path createBezierArcRadians(@NotNull PointF center, float radius, double startAngleRadians,
double sweepAngleRadians, int pointsOnCircle, boolean overlapPoints,
@Nullable Path addToPath)
{
final Path path = addToPath != null ? addToPath : new Path();
if (sweepAngleRadians == 0d) { return path; }
if (pointsOnCircle >= 1)
{
final double threshold = FULL_CIRCLE_RADIANS / pointsOnCircle;
if (abs(sweepAngleRadians) > threshold)
{
double angle = normalizeRadians(startAngleRadians);
PointF end, start = pointFromAngleRadians(center, radius, angle);
path.moveTo(start.x, start.y);
if (overlapPoints)
{
final boolean cw = sweepAngleRadians > 0; // clockwise?
final double angleEnd = angle + sweepAngleRadians;
while (true)
{
double next = (cw ? ceil(angle / threshold) : floor(angle / threshold)) * threshold;
if (angle == next) { next += threshold * (cw ? 1d : -1d); }
final boolean isEnd = cw ? angleEnd <= next : angleEnd >= next;
end = pointFromAngleRadians(center, radius, isEnd ? angleEnd : next);
addBezierArcToPath(path, center, start, end, false);
if (isEnd) { break; }
angle = next;
start = end;
}
}
else
{
final int n = abs((int)ceil(sweepAngleRadians / threshold));
final double sweep = sweepAngleRadians / n;
for (int i = 0;
i < n;
i++, start = end)
{
angle += sweep;
end = pointFromAngleRadians(center, radius, angle);
addBezierArcToPath(path, center, start, end, false);
}
}
return path;
}
}
final PointF start = pointFromAngleRadians(center, radius, startAngleRadians);
final PointF end = pointFromAngleRadians(center, radius, startAngleRadians + sweepAngleRadians);
addBezierArcToPath(path, center, start, end, true);
return path;
}
/**
* Adds a circular arc to the given path by approximating it through a cubic Bézier curve, splitting it if
* necessary. The precision of the approximation can be adjusted through {@code pointsOnCircle} and
* {@code overlapPoints} parameters.
* <p>
* <strong>Example:</strong> imagine an arc starting from 0° and sweeping 100° with a value of
* {@code pointsOnCircle} equal to 12 (threshold -> 360° / 12 = 30°):
* <ul>
* <li>if {@code overlapPoints} is {@code true}, it will be split as following:
* <ul>
* <li>from 0° to 30° (sweep 30°)</li>
* <li>from 30° to 60° (sweep 30°)</li>
* <li>from 60° to 90° (sweep 30°)</li>
* <li>from 90° to 100° (sweep 10°)</li>
* </ul>
* </li>
* <li>if {@code overlapPoints} is {@code false}, it will be split into 4 equal arcs:
* <ul>
* <li>from 0° to 25° (sweep 25°)</li>
* <li>from 25° to 50° (sweep 25°)</li>
* <li>from 50° to 75° (sweep 25°)</li>
* <li>from 75° to 100° (sweep 25°)</li>
* </ul>
* </li>
* </ul>
* </p>
* <p/>
* For a technical explanation:
* <a href="http://hansmuller-flex.blogspot.de/2011/10/more-about-approximating-circular-arcs.html">
* http://hansmuller-flex.blogspot.de/2011/10/more-about-approximating-circular-arcs.html
* </a>
*
* @param center The center of the circle.
* @param radius The radius of the circle.
* @param startAngleDegrees The starting angle on the circle (in degrees).
* @param sweepAngleDegrees How long to make the total arc (in degrees).
* @param pointsOnCircle Defines a <i>threshold</i> (360° /{@code pointsOnCircle}) to split the Bézier arc to
* better approximate a circular arc, depending also on the value of {@code overlapPoints}.
* The suggested number to have a reasonable approximation of a circle is at least 4 (90°).
* Less than 1 will ignored (the arc will not be split).
* @param overlapPoints Given the <i>threshold</i> defined through {@code pointsOnCircle}:
* <ul>
* <li>if {@code true}, split the arc on every angle which is a multiple of the
* <i>threshold</i> (yields better results if drawing precision is required,
* especially when stacking multiple arcs, but can potentially use more points)</li>
* <li>if {@code false}, split the arc equally so that each part is shorter than
* the <i>threshold</i></li>
* </ul>
* @param addToPath An existing path where to add the arc to, or {@code null} to create a new path.
*
* @return {@code addToPath} if it's not {@code null}, otherwise a new path.
*
* @see #createBezierArcRadians(android.graphics.PointF, float, double, double, int, boolean, android.graphics.Path)
*/
@NotNull
public static Path createBezierArcDegrees(@NotNull PointF center, float radius, float startAngleDegrees,
float sweepAngleDegrees, int pointsOnCircle, boolean overlapPoints,
@Nullable Path addToPath)
{
return createBezierArcRadians(center, radius, toRadians(startAngleDegrees), toRadians(sweepAngleDegrees),
pointsOnCircle, overlapPoints, addToPath);
}
}