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| Rev | Author | Line No. | Line |
|---|---|---|---|
| 907 | chris | 1 | package com.gebauz.bauzoid.math; |
| 2 | |||
| 3 | /** Line segment class. */ |
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| 4 | public class Line2 |
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| 5 | { |
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| 6 | // Constants======================================================================================== |
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| 7 | |||
| 8 | // Embedded Types=================================================================================== |
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| 9 | |||
| 10 | // Fields=========================================================================================== |
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| 11 | |||
| 12 | private float ax = 0; |
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| 13 | private float ay = 0; |
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| 14 | |||
| 15 | private float bx = 0; |
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| 16 | private float by = 0; |
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| 17 | |||
| 18 | // parametric form |
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| 19 | private float A = 0.0f; |
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| 20 | private float B = 0.0f; |
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| 21 | private float C = 0.0f; |
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| 22 | |||
| 23 | // Methods========================================================================================== |
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| 24 | |||
| 25 | public Line2() |
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| 26 | { |
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| 27 | calcParametric(); |
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| 28 | } |
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| 29 | |||
| 30 | public Line2(float _ax, float _ay, float _bx, float _by) |
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| 31 | { |
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| 32 | ax = _ax; ay = _ay; |
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| 33 | bx = _bx; by = _by; |
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| 34 | calcParametric(); |
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| 35 | } |
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| 36 | |||
| 37 | public Line2(Vector2 a, Vector2 b) |
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| 38 | { |
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| 39 | ax = a.x; ay = a.y; |
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| 40 | bx = b.x; by = b.y; |
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| 41 | calcParametric(); |
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| 42 | } |
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| 43 | |||
| 1001 | chris | 44 | public Vector2 getLineVector() |
| 45 | { |
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| 46 | return new Vector2(bx - ax, by - ay); |
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| 47 | } |
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| 48 | |||
| 907 | chris | 49 | public void calcParametric() |
| 50 | { |
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| 51 | A = getA(); |
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| 52 | B = getB(); |
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| 53 | C = getC(); |
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| 54 | } |
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| 55 | |||
| 56 | public float getLengthSqr() |
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| 57 | { |
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| 58 | float diffX = ax - bx; |
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| 59 | float diffY = ay - by; |
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| 60 | return (diffX*diffX + diffY*diffY); |
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| 61 | } |
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| 62 | |||
| 63 | public float getLength() |
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| 64 | { |
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| 65 | float length = getLengthSqr(); |
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| 66 | return (float)(Math.sqrt(length)); |
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| 67 | } |
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| 68 | |||
| 69 | /** Check if x, y (which must be collinear to the line segment) lies within the line segment. */ |
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| 70 | public boolean isCollinearPointOnSegment(float x, float y) |
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| 71 | { |
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| 72 | if ((x <= Math.max(ax, bx)) && (x >= Math.min(ax, bx)) && |
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| 73 | (y <= Math.max(ay, by)) && (y >= Math.min(ay, by))) |
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| 74 | { |
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| 75 | return true; |
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| 76 | } |
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| 77 | |||
| 78 | return false; |
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| 79 | } |
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| 80 | |||
| 81 | /** Get the A coefficient in the Ax + By = C form. */ |
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| 82 | public final float getA() |
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| 83 | { |
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| 84 | return by - ay; |
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| 85 | } |
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| 86 | |||
| 87 | /** Get the B coefficient in the Ax + By = C form. */ |
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| 88 | public final float getB() |
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| 89 | { |
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| 90 | return ax - bx; |
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| 91 | } |
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| 92 | |||
| 93 | /** Get the C coefficient in the Ax + By = C form. */ |
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| 94 | public final float getC() |
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| 95 | { |
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| 96 | return getA() * ax + getB() * ay; |
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| 97 | } |
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| 98 | |||
| 99 | public Vector2 getLineIntersection(Line2 other) |
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| 100 | { |
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| 101 | // get Ax + By = C form coefficients |
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| 102 | float A1 = A; |
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| 103 | float B1 = B; |
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| 104 | float C1 = C; |
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| 105 | |||
| 106 | float A2 = other.A; |
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| 107 | float B2 = other.B; |
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| 108 | float C2 = other.C; |
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| 109 | |||
| 110 | float delta = A1*B2 - A2*B1; |
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| 111 | if (delta == 0) |
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| 112 | return null; |
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| 113 | |||
| 114 | float x = (B2*C1 - B1*C2)/delta; |
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| 115 | float y = (A1*C2 - A2*C1)/delta; |
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| 116 | |||
| 117 | return new Vector2(x, y); |
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| 118 | } |
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| 119 | |||
| 120 | public Vector2 getSegmentIntersection(Line2 other) |
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| 121 | { |
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| 122 | Vector2 p = getLineIntersection(other); |
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| 123 | |||
| 124 | if (p == null) |
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| 125 | return null; |
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| 126 | |||
| 127 | if (this.isCollinearPointOnSegment(p.x, p.y) && other.isCollinearPointOnSegment(p.x, p.y)) |
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| 128 | return p; |
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| 129 | |||
| 130 | return null; |
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| 131 | } |
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| 132 | |||
| 133 | public boolean intersectsSegment(Line2 other) |
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| 134 | { |
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| 135 | Vector2 p = getSegmentIntersection(other); |
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| 136 | |||
| 137 | if (p == null) |
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| 138 | return false; |
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| 139 | |||
| 140 | return true; |
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| 141 | } |
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| 1001 | chris | 142 | |
| 143 | /** Get the smallest perpendicular vector from point to the line. */ |
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| 144 | public Vector2 getMinimalVectorFrom(Vector2 point) |
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| 145 | { |
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| 146 | Vector2 closestPoint = getClosestPointFrom(point); |
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| 147 | |||
| 148 | return new Vector2(closestPoint.x - point.x, closestPoint.y - point.y); |
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| 149 | } |
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| 150 | |||
| 151 | /** Get the smallest perpendicular vector from point to the line. */ |
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| 152 | public Vector2 getMinimalVectorFrom(float px, float py) |
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| 153 | { |
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| 154 | return getMinimalVectorFrom(new Vector2(px, py)); |
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| 155 | } |
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| 156 | |||
| 157 | /** Get the closest point on line from a given point. */ |
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| 158 | public Vector2 getClosestPointFrom(Vector2 point) |
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| 159 | { |
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| 160 | Vector2 ab = getLineVector(); |
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| 161 | |||
| 162 | Vector2 ap = new Vector2(point.x - ax, point.y - ay); |
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| 163 | |||
| 164 | float t = Vector2.dotProduct(ap, ab) / ab.squaredLength(); |
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| 165 | |||
| 166 | t = MathUtil.clamp(t, 0, 1); |
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| 167 | |||
| 168 | return new Vector2(ax + t * ab.x, ay + t * ab.y); |
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| 169 | } |
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| 170 | |||
| 171 | public Vector2 getClosestPointFrom(float px, float py) |
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| 172 | { |
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| 173 | return getClosestPointFrom(new Vector2(px, py)); |
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| 174 | } |
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| 175 | |||
| 176 | |||
| 177 | /* |
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| 178 | (P-A).D == |X-A| |
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| 907 | chris | 179 | |
| 1001 | chris | 180 | X == A + ((P-A).D)D |
| 181 | Desired perpendicular: X-P |
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| 182 | |||
| 183 | |||
| 184 | Returns the closest point x on segment ab to point p |
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| 185 | (x-p).(b-a) = 0, x = a + t(b-a) |
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| 186 | => (a + t(b-a) - p).(b-a) = 0 |
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| 187 | => t(b-a).(b-a) = (p-a).(b-a) |
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| 188 | => t = (p-a).(b-a) / |b-a|^2 |
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| 189 | |||
| 190 | Ogre::Vector3 closestPointOnLineSegment(const Ogre::Vector3 &p,const Ogre::Vector3 &a,const Ogre::Vector3 b) |
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| 191 | { |
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| 192 | Ogre::Vector3 ab = b-a; |
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| 193 | float t = (p-a).dotProduct(ab) / (ab).squaredLength(); |
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| 194 | t = Ogre::Math::Clamp(t,0.f,1.f); |
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| 195 | return a + t*ab; |
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| 196 | } |
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| 197 | |||
| 198 | * |
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| 199 | * |
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| 200 | * |
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| 201 | */ |
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| 202 | |||
| 907 | chris | 203 | // Getters/Setters================================================================================== |
| 204 | |||
| 205 | } |
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| 206 | |||
| 207 | |||
| 208 |