1.1 --- a/geometry.cpp Wed Jan 16 15:45:19 2008 +0000
1.2 +++ b/geometry.cpp Wed Jan 16 15:45:19 2008 +0000
1.3 @@ -1,5 +1,7 @@
1.4 #include "geometry.h"
1.5
1.6 +#include <math.h>
1.7 +
1.8
1.9 QRectF addBBox(QRectF r1, QRectF r2)
1.10 {
1.11 @@ -39,3 +41,180 @@
1.12 return true;
1.13 return false;
1.14 }
1.15 +
1.16 +QPointF normalize (const QPointF &p)
1.17 +{
1.18 + qreal n=sqrt ( p.x()*p.x() + p.y()*p.y() );
1.19 + return QPointF (p.x()/n,p.y()/n);
1.20 +}
1.21 +
1.22 +// Dot product of two vectors
1.23 +qreal dotProduct (const QPointF &a, const QPointF &b)
1.24 +{
1.25 + return a.x()*b.x() + a.y()*b.y();
1.26 +}
1.27 +
1.28 +// Structure that stores the results of the PolygonCollision function
1.29 +class PolygonCollisionResult {
1.30 +public:
1.31 + // Are the polygons going to intersect forward in time?
1.32 + bool WillIntersect;
1.33 +
1.34 + // Are the polygons currently intersecting?
1.35 + bool Intersect;
1.36 +
1.37 + // The translation to apply to the first polygon to push the polygons apart.
1.38 + QPointF MinimumTranslationVector;
1.39 +};
1.40 +
1.41 +
1.42 +/* Calculate the projection of a polygon on an axis
1.43 + and returns it as a [min, max] interval
1.44 +*/
1.45 +void ProjectPolygon(QPointF axis, QPolygonF polygon, qreal &min, qreal &max)
1.46 +{
1.47 + // To project a point on an axis use the dot product
1.48 +
1.49 + qreal d = dotProduct(axis,polygon.at(0));
1.50 + min = d;
1.51 + max = d;
1.52 + for (int i = 0; i < polygon.size(); i++) {
1.53 + d= dotProduct (polygon.at(i),axis);
1.54 + if (d < min)
1.55 + min = d;
1.56 + else
1.57 + {
1.58 + if (d> max) max = d;
1.59 + }
1.60 + }
1.61 +}
1.62 +
1.63 +/* Calculate the signed distance between [minA, maxA] and [minB, maxB]
1.64 + The distance will be negative if the intervals overlap
1.65 +*/
1.66 +
1.67 +
1.68 +qreal intervalDistance(qreal minA, qreal maxA, qreal minB, qreal maxB) {
1.69 + if (minA < minB) {
1.70 + return minB - maxA;
1.71 + } else {
1.72 + return minA - maxB;
1.73 + }
1.74 +}
1.75 +/*
1.76 + Check if polygon A is going to collide with polygon B.
1.77 + The last parameter is the *relative* velocity
1.78 + of the polygons (i.e. velocityA - velocityB)
1.79 +
1.80 +*/
1.81 +PolygonCollisionResult PolygonCollision(QPolygonF polygonA,
1.82 + QPolygonF polygonB, QPointF velocity) {
1.83 + PolygonCollisionResult result;
1.84 + result.Intersect = true;
1.85 + result.WillIntersect = true;
1.86 +
1.87 + int edgeCountA = polygonA.size();
1.88 + int edgeCountB = polygonB.size();
1.89 + qreal minIntervalDistance = 1000000000;
1.90 + QPointF translationAxis;
1.91 + QPointF edge;
1.92 +
1.93 + // Loop through all the edges of both polygons
1.94 +
1.95 + for (int i=0; i < edgeCountA + edgeCountB; i++)
1.96 + {
1.97 + if (i< edgeCountA)
1.98 + edge = polygonA.at(i);
1.99 + else
1.100 + edge = polygonB.at(i - edgeCountA);
1.101 +
1.102 + // ===== 1. Find if the polygons are currently intersecting =====
1.103 +
1.104 +
1.105 + // Find the axis perpendicular to the current edge
1.106 +
1.107 + QPointF axis (-edge.y(), edge.x());
1.108 + normalize(axis);
1.109 +
1.110 + // Find the projection of the polygon on the current axis
1.111 +
1.112 + qreal minA = 0; qreal minB = 0; qreal maxA = 0; qreal maxB = 0;
1.113 + ProjectPolygon(axis, polygonA, minA, maxA);
1.114 + ProjectPolygon(axis, polygonB, minB, maxB);
1.115 +
1.116 + // Check if the polygon projections are currentlty intersecting
1.117 +
1.118 + if (intervalDistance(minA, maxA, minB, maxB) > 0)\
1.119 + result.Intersect = false;
1.120 +
1.121 + // ===== 2. Now find if the polygons *will* intersect =====
1.122 +
1.123 +
1.124 + // Project the velocity on the current axis
1.125 +
1.126 + qreal velocityProjection = dotProduct(axis,velocity);
1.127 +
1.128 + // Get the projection of polygon A during the movement
1.129 +
1.130 + if (velocityProjection < 0) {
1.131 + minA += velocityProjection;
1.132 + } else {
1.133 + maxA += velocityProjection;
1.134 + }
1.135 +
1.136 + // Do the same test as above for the new projection
1.137 +
1.138 + qreal d = intervalDistance(minA, maxA, minB, maxB);
1.139 + if (d > 0) result.WillIntersect = false;
1.140 +
1.141 + // If the polygons are not intersecting and won't intersect, exit the loop
1.142 +
1.143 + if (!result.Intersect && !result.WillIntersect) break;
1.144 +
1.145 + // Check if the current interval distance is the minimum one. If so store
1.146 + // the interval distance and the current distance.
1.147 + // This will be used to calculate the minimum translation vector
1.148 +
1.149 + if (d<0) d=-d;
1.150 + if (d < minIntervalDistance) {
1.151 + minIntervalDistance = d;
1.152 + translationAxis = axis;
1.153 +
1.154 + //QPointF t = polygonA.Center - polygonB.Center;
1.155 + QPointF t = polygonA.at(0) - polygonB.at(0);
1.156 + if (dotProduct(t,translationAxis) < 0)
1.157 + translationAxis = -translationAxis;
1.158 + }
1.159 + }
1.160 +
1.161 + // The minimum translation vector
1.162 + // can be used to push the polygons appart.
1.163 +
1.164 + if (result.WillIntersect)
1.165 + result.MinimumTranslationVector =
1.166 + translationAxis * minIntervalDistance;
1.167 +
1.168 + return result;
1.169 +}
1.170 +
1.171 +/* The function can be used this way:
1.172 + QPointF polygonATranslation = new QPointF();
1.173 +*/
1.174 +
1.175 +
1.176 +/*
1.177 +PolygonCollisionResult r = PolygonCollision(polygonA, polygonB, velocity);
1.178 +
1.179 +if (r.WillIntersect)
1.180 + // Move the polygon by its velocity, then move
1.181 + // the polygons appart using the Minimum Translation Vector
1.182 + polygonATranslation = velocity + r.MinimumTranslationVector;
1.183 +else
1.184 + // Just move the polygon by its velocity
1.185 + polygonATranslation = velocity;
1.186 +
1.187 +polygonA.Offset(polygonATranslation);
1.188 +
1.189 +*/
1.190 +
1.191 +