ShaheenGandhi.pde

   1 import toxi.geom.Vec3D;
   2 import toxi.geom.Matrix4x4;
   3
   4 class HelixPattern extends SCPattern {
   5
   6   // Stores a line in point + vector form
   7   private class Line {
   8     private final PVector origin;
   9     private final PVector vector;
  10
  11     Line(PVector pt, PVector v) {
  12       origin = pt;
  13       vector = v.get();
  14       vector.normalize();
  15     }
  16
  17     PVector getPoint() {
  18       return origin;
  19     }
  20
  21     PVector getVector() {
  22       return vector;
  23     }
  24
  25     PVector getPointAt(final float t) {
  26       return PVector.add(origin, PVector.mult(vector, t));
  27     }
  28
  29     boolean isColinear(final PVector pt) {
  30       PVector projected = projectPoint(pt);
  31       return projected.x==pt.x && projected.y==pt.y && projected.z==pt.z;
  32     }
  33
  34     float getTValue(final PVector pt) {
  35       PVector subtraction = PVector.sub(pt, origin);
  36       return subtraction.dot(vector);
  37     }
  38
  39     PVector projectPoint(final PVector pt) {
  40       return getPointAt(getTValue(pt));
  41     }
  42
  43     PVector rotatePoint(final PVector p, final float t) {
  44       final PVector o = origin;
  45       final PVector v = vector;
  46
  47       final float cost = cos(t);
  48       final float sint = sin(t);
  49
  50       float x = (o.x*(v.y*v.y + v.z*v.z) - v.x*(o.y*v.y + o.z*v.z - v.x*p.x - v.y*p.y - v.z*p.z))*(1 - cost) + p.x*cost + (-o.z*v.y + o.y*v.z - v.z*p.y + v.y*p.z)*sint;
  51       float y = (o.y*(v.x*v.x + v.z*v.z) - v.y*(o.x*v.x + o.z*v.z - v.x*p.x - v.y*p.y - v.z*p.z))*(1 - cost) + p.y*cost + (o.z*v.x - o.x*v.z + v.z*p.x - v.x*p.z)*sint;
  52       float z = (o.z*(v.x*v.x + v.y*v.y) - v.z*(o.x*v.x + o.y*v.y - v.x*p.x - v.y*p.y - v.z*p.z))*(1 - cost) + p.z*cost + (-o.y*v.x + o.x*v.y - v.y*p.x + v.x*p.y)*sint;
  53       return new PVector(x, y, z);
  54     }
  55   }
  56
  57   private class Helix {
  58     private final Line axis;
  59     private final float period; // period of coil
  60     private final float rotationPeriod; // animation period
  61     private final float radius; // radius of coil
  62     private final float girth; // girth of coil
  63     private final PVector referencePoint;
  64     private float phase;
  65     private PVector phaseNormal;
  66
  67     Helix(Line axis, float period, float radius, float girth, float phase, float rotationPeriod) {
  68       this.axis = axis;
  69       this.period = period;
  70       this.radius = radius;
  71       this.girth = girth;
  72       this.phase = phase;
  73       this.rotationPeriod = rotationPeriod;
  74
  75       // Generate a normal that will rotate to
  76       // produce the helical shape.
  77       PVector pt = new PVector(0, 1, 0);
  78       if (this.axis.isColinear(pt)) {
  79         pt = new PVector(0, 0, 1);
  80         if (this.axis.isColinear(pt)) {
  81           pt = new PVector(0, 1, 1);
  82         }
  83       }
  84
  85       this.referencePoint = pt;
  86
  87       // The normal is calculated by the cross product of the axis
  88       // and a random point that is not colinear with it.
  89       phaseNormal = axis.getVector().cross(referencePoint);
  90       phaseNormal.normalize();
  91       phaseNormal.mult(radius);
  92     }
  93
  94     Line getAxis() {
  95       return axis;
  96     }
  97
  98     PVector getPhaseNormal() {
  99       return phaseNormal;
 100     }
 101
 102     float getPhase() {
 103       return phase;
 104     }
 105
 106     void step(int deltaMs) {
 107       // Rotate
 108       if (rotationPeriod != 0) {
 109         this.phase = (phase + ((float)deltaMs / (float)rotationPeriod) * TWO_PI);
 110       }
 111     }
 112
 113     PVector pointOnToroidalAxis(float t) {
 114       PVector p = axis.getPointAt(t);
 115       PVector middle = PVector.add(p, phaseNormal);
 116       return axis.rotatePoint(middle, (t / period) * TWO_PI + phase);
 117     }
 118
 119     private float myDist(PVector p1, PVector p2) {
 120       final float x = p2.x-p1.x;
 121       final float y = p2.y-p1.y;
 122       final float z = p2.z-p1.z;
 123       return sqrt(x*x + y*y + z*z);
 124     }
 125
 126     color colorOfPoint(final PVector p) {
 127       final float t = axis.getTValue(p);
 128       final PVector axisPoint = axis.getPointAt(t);
 129
 130       // For performance reasons, cut out points that are outside of
 131       // the tube where the toroidal coil lives.
 132       if (abs(myDist(p, axisPoint) - radius) > girth*.5f) {
 133         return color(0,0,0);
 134       }
 135
 136       // Find the appropriate point for the current rotation
 137       // of the helix.
 138       PVector toroidPoint = axisPoint;
 139       toroidPoint.add(phaseNormal);
 140       toroidPoint = axis.rotatePoint(toroidPoint, (t / period) * TWO_PI + phase);
 141
 142       // The rotated point represents the middle of the girth of
 143       // the helix.  Figure out if the current point is inside that
 144       // region.
 145       float d = myDist(p, toroidPoint);
 146
 147       // Soften edges by fading brightness.
 148       float b = constrain(100*(1 - ((d-.5*girth)/(girth*.5))), 0, 100);
 149       return color((lx.getBaseHuef() + (360*(phase / TWO_PI)))%360, 80, b);
 150     }
 151   }
 152
 153   private final Helix h1;
 154   private final Helix h2;
 155   private final Line[] basePairs;
 156
 157   private final BasicParameter helix1On = new BasicParameter("H1ON", 1);
 158   private final BasicParameter helix2On = new BasicParameter("H2ON", 1);
 159   private final BasicParameter basePairsOn = new BasicParameter("BPON", 1);
 160
 161   private static final float helixCoilPeriod = 100;
 162   private static final float helixCoilRadius = 45;
 163   private static final float helixCoilGirth = 20;
 164   private static final float helixCoilRotationPeriod = 10000;
 165
 166   private static final float spokePeriod = 40;
 167   private static final float spokeGirth = 10;
 168   private static final float spokePhase = 10;
 169   private static final float spokeRadius = 35; // helixCoilRadius - helixCoilGirth*.5f;
 170
 171   private static final float tMin = -200;
 172   private static final float tMax = 200;
 173
 174   public HelixPattern(GLucose glucose) {
 175     super(glucose);
 176
 177     addParameter(helix1On);
 178     addParameter(helix2On);
 179     addParameter(basePairsOn);
 180
 181     PVector origin = new PVector(100, 50, 45);
 182     PVector axis = new PVector(1,0,0);
 183
 184     h1 = new Helix(
 185       new Line(origin, axis),
 186       helixCoilPeriod,
 187       helixCoilRadius,
 188       helixCoilGirth,
 189       0,
 190       helixCoilRotationPeriod);
 191     h2 = new Helix(
 192       new Line(origin, axis),
 193       helixCoilPeriod,
 194       helixCoilRadius,
 195       helixCoilGirth,
 196       PI,
 197       helixCoilRotationPeriod);
 198
 199     basePairs = new Line[(int)floor((tMax - tMin)/spokePeriod)];
 200   }
 201
 202   private void calculateSpokes() {
 203     for (float t = tMin + spokePhase; t < tMax; t += spokePeriod) {
 204       int spokeIndex = (int)floor((t - tMin)/spokePeriod);
 205       PVector h1point = h1.pointOnToroidalAxis(t);
 206       PVector spokeCenter = h1.getAxis().getPointAt(t);
 207       PVector spokeVector = PVector.sub(h1point, spokeCenter);
 208       basePairs[spokeIndex] = new Line(spokeCenter, spokeVector);
 209     }
 210   }
 211
 212   private color calculateSpokeColor(final PVector pt) {
 213     // Find the closest spoke's t-value and calculate its
 214     // axis.  Until everything animates in the model reference
 215     // frame, this has to be calculated at every step because
 216     // the helices rotate.
 217     Line axis = h1.getAxis();
 218     float t = axis.getTValue(pt) + spokePhase;
 219     int spokeIndex = (int)floor((t - tMin + spokePeriod/2) / spokePeriod);
 220     if (spokeIndex < 0 || spokeIndex >= basePairs.length) {
 221       return color(0,0,0);
 222     }
 223     Line spokeLine = basePairs[spokeIndex];
 224     PVector pointOnSpoke = spokeLine.projectPoint(pt);
 225     float b = ((PVector.dist(pt, pointOnSpoke) < spokeGirth) && (PVector.dist(pointOnSpoke, spokeLine.getPoint()) < spokeRadius)) ? 100.f : 0.f;
 226     return color(100, 80.f, b);
 227   }
 228
 229   void run(int deltaMs) {
 230     boolean h1on = helix1On.getValue() > 0.5;
 231     boolean h2on = helix2On.getValue() > 0.5;
 232     boolean spokesOn = (float)basePairsOn.getValue() > 0.5;
 233
 234     h1.step(deltaMs);
 235     h2.step(deltaMs);
 236     calculateSpokes();
 237
 238     for (Point p : model.points) {
 239       PVector pt = new PVector(p.x,p.y,p.z);
 240       color h1c = h1.colorOfPoint(pt);
 241       color h2c = h2.colorOfPoint(pt);
 242       color spokeColor = calculateSpokeColor(pt);
 243
 244       if (!h1on) {
 245         h1c = color(0,0,0);
 246       }
 247
 248       if (!h2on) {
 249         h2c = color(0,0,0);
 250       }
 251
 252       if (!spokesOn) {
 253         spokeColor = color(0,0,0);
 254       }
 255
 256       // The helices are positioned to not overlap.  If that changes,
 257       // a better blending formula is probably needed.
 258       colors[p.index] = blendColor(blendColor(h1c, h2c, ADD), spokeColor, ADD);
 259     }
 260   }
 261 }
 262