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engines/sword25/math/line.h

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+/* ScummVM - Graphic Adventure Engine
+ *
+ * ScummVM is the legal property of its developers, whose names
+ * are too numerous to list here. Please refer to the COPYRIGHT
+ * file distributed with this source distribution.
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ *
+ */
+
+/*
+ * This code is based on Broken Sword 2.5 engine
+ *
+ * Copyright (c) Malte Thiesen, Daniel Queteschiner and Michael Elsdoerfer
+ *
+ * Licensed under GNU GPL v2
+ *
+ */
+
+/*
+	BS_Line
+	-------
+	This class contains only static methods, which have to do with straight line
+	segments. There is no real straight line segment class. Calculations will be
+	used with polygons, and it is important the process of starting and selecting
+	endpoints of lines is dynamic. This would prhobit a polygon from a set
+	being formed by fixed line segments
+
+	Autor: Malte Thiesen
+*/
+
+#ifndef SWORD25_LINE_H
+#define SWORD25_LINE_H
+
+#include "sword25/kernel/common.h"
+
+namespace Sword25 {
+
+class Line {
+public:
+	/**
+	 * Determines whether a piont is left of a line
+	 * @param a         The start point of a line
+	 * @param b         The end point of a line
+	 * @param c         The test point
+	 * @return          Returns true if the point is to the left of the line.
+	 * If the point is to the right of the line or on the line, false is returned.
+	 */
+	static bool isVertexLeft(const Vertex &a, const Vertex &b, const Vertex &c) {
+		return triangleArea2(a, b, c) > 0;
+	}
+
+	static bool isVertexLeftOn(const Vertex &a, const Vertex &b, const Vertex &c) {
+		return triangleArea2(a, b, c) >= 0;
+	}
+
+	/**
+	 * Determines whether a piont is right of a line
+	 * @param a         The start point of a line
+	 * @param b         The end point of a line
+	 * @param c         The test point
+	 * @return          Returns true if the point is to the right of the line.
+	 * If the point is to the right of the line or on the line, false is returned.
+	 */
+	static bool isVertexRight(const Vertex &a, const Vertex &b, const Vertex &c) {
+		return triangleArea2(a, b, c) < 0;
+	}
+
+	static bool isVertexRightOn(const Vertex &a, const Vertex &b, const Vertex &c) {
+		return triangleArea2(a, b, c) <= 0;
+	}
+
+	/**
+	 * Determines whether a piont is on a line
+	 * @param a         The start point of a line
+	 * @param b         The end point of a line
+	 * @param c         The test point
+	 * @return          Returns true if the point is on the line, false otherwise.
+	 */
+	static bool isVertexOn(const Vertex &a, const Vertex &b, const Vertex &c) {
+		return triangleArea2(a, b, c) == 0;
+	}
+
+	enum VERTEX_CLASSIFICATION {
+		LEFT,
+		RIGHT,
+		ON
+	};
+
+	/**
+	 * Determines where a point is relative to a line.
+	 * @param a         The start point of a line
+	 * @param b         The end point of a line
+	 * @param c         The test point
+	 * @return          LEFT is returned if the point is to the left of the line.
+	 * RIGHT is returned if the point is to the right of the line.
+	 * ON is returned if the point is on the line.
+	 */
+	static VERTEX_CLASSIFICATION classifyVertexToLine(const Vertex &a, const Vertex &b, const Vertex &c) {
+		int area = triangleArea2(a, b, c);
+		if (area > 0) return LEFT;
+		if (area < 0) return RIGHT;
+		return ON;
+	}
+
+	/**
+	 * Determines whether two lines intersect
+	 * @param a         The start point of the first line
+	 * @param b         The end point of the first line
+	 * @param c         The start point of the second line
+	 * @param d         The end point of the second line
+	 * @remark          In cases where a line only touches the other, false is returned (improper intersection)
+	 */
+	static bool doesIntersectProperly(const Vertex &a, const Vertex &b, const Vertex &c, const Vertex &d) {
+		VERTEX_CLASSIFICATION class1 = classifyVertexToLine(a, b, c);
+		VERTEX_CLASSIFICATION class2 = classifyVertexToLine(a, b, d);
+		VERTEX_CLASSIFICATION class3 = classifyVertexToLine(c, d, a);
+		VERTEX_CLASSIFICATION class4 = classifyVertexToLine(c, d, b);
+
+		if (class1 == ON || class2 == ON || class3 == ON || class4 == ON) return false;
+
+		return ((class1 == LEFT) ^(class2 == LEFT)) && ((class3 == LEFT) ^(class4 == LEFT));
+	}
+
+	/**
+	 * Determines whether a point is on a line segment
+	 * @param a         The start point of a line
+	 * @param b         The end point of a line
+	 * @param c         The test point
+	 */
+	static bool isOnLine(const Vertex &a, const Vertex &b, const Vertex &c) {
+		// The items must all be Collinear, otherwise don't bothering testing the point
+		if (triangleArea2(a, b, c) != 0) return false;
+
+		// If the line segment is not vertical, check on the x-axis, otherwise the y-axis
+		if (a.x != b.x) {
+			return ((a.x <= c.x) &&
+			        (c.x <= b.x)) ||
+			       ((a.x >= c.x) &&
+			        (c.x >= b.x));
+		} else {
+			return ((a.y <= c.y) &&
+			        (c.y <= b.y)) ||
+			       ((a.y >= c.y) &&
+			        (c.y >= b.y));
+		}
+	}
+
+	static bool isOnLineStrict(const Vertex &a, const Vertex &b, const Vertex &c) {
+		// The items must all be Collinear, otherwise don't bothering testing the point
+		if (triangleArea2(a, b, c) != 0) return false;
+
+		// If the line segment is not vertical, check on the x-axis, otherwise the y-axis
+		if (a.x != b.x) {
+			return ((a.x < c.x) &&
+			        (c.x < b.x)) ||
+			       ((a.x > c.x) &&
+			        (c.x > b.x));
+		} else {
+			return ((a.y < c.y) &&
+			        (c.y < b.y)) ||
+			       ((a.y > c.y) &&
+			        (c.y > b.y));
+		}
+	}
+
+private:
+	/**
+	 * Return double the size of the triangle defined by the three passed points.
+	 *
+	 * The result is positive if the points are arrange counterclockwise,
+	 * and negative if they are arranged counter-clockwise.
+	 */
+	static int triangleArea2(const Vertex &a, const Vertex &b, const Vertex &c) {
+		return a.x * b.y - a.y * b.x +
+		       a.y * c.x - a.x * c.y +
+		       b.x * c.y - c.x * b.y;
+	}
+};
+
+} // End of namespace Sword25
+
+#endif