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     void step(int deltaMs) {
  99       // Rotate
 100       if (rotationPeriod != 0) {
 101         this.phase = (phase + ((float)deltaMs / (float)rotationPeriod) * TWO_PI);
 102       }
 103     }
 104
 105     PVector pointOnToroidalAxis(float t) {
 106       PVector p = axis.getPointAt(t);
 107       PVector middle = PVector.add(p, phaseNormal);
 108       return axis.rotatePoint(middle, (t / period) * TWO_PI + phase);
 109     }
 110
 111     color colorOfPoint(final PVector p) {
 112       float t = axis.getTValue(p);
 113
 114       // For performance reasons, cut out points that are outside of
 115       // the tube where the toroidal coil lives.
 116       if (abs(PVector.dist(p, axis.getPointAt(t)) - radius) > girth*.5f) {
 117         return color(0,0,0);
 118       }
 119
 120       // Find the appropriate point for the current rotation
 121       // of the helix.
 122       PVector toroidPoint = pointOnToroidalAxis(t);
 123
 124       // The rotated point represents the middle of the girth of
 125       // the helix.  Figure out if the current point is inside that
 126       // region.
 127       float d = PVector.dist(p, toroidPoint);
 128
 129       // Soften edges by fading brightness.
 130       float b = constrain(100*(1 - ((d-.5*girth)/(girth*.5))), 0, 100);
 131       return color((lx.getBaseHuef() + (360*(phase / TWO_PI)))%360, 80, b);
 132     }
 133   }
 134
 135   private final Helix h1;
 136   private final Helix h2;
 137
 138   private final BasicParameter helix1On = new BasicParameter("H1ON", 1);
 139   private final BasicParameter helix2On = new BasicParameter("H2ON", 1);
 140   private final BasicParameter basePairsOn = new BasicParameter("BPON", 1);
 141
 142   private static final float helixCoilPeriod = 100;
 143   private static final float helixCoilRadius = 45;
 144   private static final float helixCoilGirth = 20;
 145   private static final float helixCoilRotationPeriod = 10000;
 146
 147   private static final float spokePeriod = 40;
 148   private static final float spokeGirth = 10;
 149   private static final float spokePhase = 10;
 150   private static final float spokeRadius = 35; // helixCoilRadius - helixCoilGirth*.5f;
 151
 152   public HelixPattern(GLucose glucose) {
 153     super(glucose);
 154
 155     addParameter(helix1On);
 156     addParameter(helix2On);
 157     addParameter(basePairsOn);
 158
 159     PVector origin = new PVector(100, 50, 45);
 160     PVector axis = new PVector(1,0,0);
 161
 162     h1 = new Helix(
 163       new Line(origin, axis),
 164       helixCoilPeriod,
 165       helixCoilRadius,
 166       helixCoilGirth,
 167       0,
 168       helixCoilRotationPeriod);
 169     h2 = new Helix(
 170       new Line(origin, axis),
 171       helixCoilPeriod,
 172       helixCoilRadius,
 173       helixCoilGirth,
 174       PI,
 175       helixCoilRotationPeriod);
 176   }
 177
 178   private color calculateSpokeColor(final color h1c, final color h2c, final PVector pt) {
 179     // Find the closest spoke's t-value and calculate its
 180     // axis.  Until everything animates in the model reference
 181     // frame, this has to be calculated at every step because
 182     // the helices rotate.
 183     float t = h1.getAxis().getTValue(pt) + spokePhase;
 184     float spokeAxisTValue = floor(((t + spokePeriod/2) / spokePeriod)) * spokePeriod;
 185     PVector h1point = h1.pointOnToroidalAxis(spokeAxisTValue);
 186     // TODO(shaheen) investigate why h1.getAxis().getPointAt(spokeAxisTValue) doesn't quite
 187     // have the same value as finding the middle between h1point and h2point.
 188     PVector spokeCenter = h1.getAxis().getPointAt(spokeAxisTValue);
 189     PVector spokeVector = PVector.sub(h1point, spokeCenter);
 190     spokeVector.normalize();
 191     Line spokeLine = new Line(h1point, spokeVector);
 192     PVector pointOnSpoke = spokeLine.projectPoint(pt);
 193     float b = ((PVector.dist(pt, pointOnSpoke) < spokeGirth) && (PVector.dist(pointOnSpoke, spokeCenter) < spokeRadius)) ? 100.f : 0.f;
 194     return color(100, 80.f, b);
 195   }
 196
 197   void run(int deltaMs) {
 198     boolean h1on = helix1On.getValue() > 0.5;
 199     boolean h2on = helix2On.getValue() > 0.5;
 200     boolean spokesOn = (float)basePairsOn.getValue() > 0.5;
 201
 202     h1.step(deltaMs);
 203     h2.step(deltaMs);
 204
 205     for (Point p : model.points) {
 206       PVector pt = new PVector(p.x,p.y,p.z);
 207       color h1c = h1.colorOfPoint(pt);
 208       color h2c = h2.colorOfPoint(pt);
 209       color spokeColor = calculateSpokeColor(h1c, h2c, pt);
 210
 211       if (!h1on) {
 212         h1c = color(0,0,0);
 213       }
 214
 215       if (!h2on) {
 216         h2c = color(0,0,0);
 217       }
 218
 219       if (!spokesOn) {
 220         spokeColor = color(0,0,0);
 221       }
 222
 223       // The helices are positioned to not overlap.  If that changes,
 224       // a better blending formula is probably needed.
 225       colors[p.index] = blendColor(blendColor(h1c, h2c, ADD), spokeColor, ADD);
 226     }
 227   }
 228 }
 229