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       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 - cos(t)) + p.x*cos(t) + (-o.z*v.y + o.y*v.z - v.z*p.y + v.y*p.z)*sin(t);
  48       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 - cos(t)) + p.y*cos(t) + (o.z*v.x - o.x*v.z + v.z*p.x - v.x*p.z)*sin(t);
  49       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 - cos(t)) + p.z*cos(t) + (-o.y*v.x + o.x*v.y - v.y*p.x + v.x*p.y)*sin(t);
  50       return new PVector(x, y, z);
  51     }
  52   }
  53
  54   private class Helix {
  55     private final Line axis;
  56     private final float period; // period of coil
  57     private final float rotationPeriod; // animation period
  58     private final float radius; // radius of coil
  59     private final float girth; // girth of coil
  60     private final PVector referencePoint;
  61     private float phase;
  62     private PVector phaseNormal;
  63
  64     Helix(Line axis, float period, float radius, float girth, float phase, float rotationPeriod) {
  65       this.axis = axis;
  66       this.period = period;
  67       this.radius = radius;
  68       this.girth = girth;
  69       this.phase = phase;
  70       this.rotationPeriod = rotationPeriod;
  71
  72       // Generate a normal that will rotate to
  73       // produce the helical shape.
  74       PVector pt = new PVector(0, 1, 0);
  75       if (this.axis.isColinear(pt)) {
  76         pt = new PVector(0, 0, 1);
  77         if (this.axis.isColinear(pt)) {
  78           pt = new PVector(0, 1, 1);
  79         }
  80       }
  81
  82       this.referencePoint = pt;
  83
  84       // The normal is calculated by the cross product of the axis
  85       // and a random point that is not colinear with it.
  86       phaseNormal = axis.getVector().cross(referencePoint);
  87       phaseNormal.normalize();
  88       phaseNormal.mult(radius);
  89     }
  90
  91     Line getAxis() {
  92       return axis;
  93     }
  94
  95     void step(int deltaMs) {
  96       // Rotate
  97       if (rotationPeriod != 0) {
  98         this.phase = (phase + ((float)deltaMs / (float)rotationPeriod) * TWO_PI);
  99       }
 100     }
 101
 102     PVector pointOnToroidalAxis(float t) {
 103       PVector p = axis.getPointAt(t);
 104       PVector middle = PVector.add(p, phaseNormal);
 105       return axis.rotatePoint(middle, (t / period) * TWO_PI + phase);
 106     }
 107
 108     color colorOfPoint(final PVector p) {
 109       float t = axis.getTValue(p);
 110
 111       // For performance reasons, cut out points that are outside of
 112       // the tube where the toroidal coil lives.
 113       if (abs(PVector.dist(p, axis.getPointAt(t)) - radius) > girth*.5f) {
 114         return color(0,0,0);
 115       }
 116
 117       // Find the appropriate point for the current rotation
 118       // of the helix.
 119       PVector toroidPoint = pointOnToroidalAxis(t);
 120
 121       // The rotated point represents the middle of the girth of
 122       // the helix.  Figure out if the current point is inside that
 123       // region.
 124       float d = PVector.dist(p, toroidPoint);
 125
 126       // Soften edges by fading brightness.
 127       float b = constrain(100*(1 - ((d-.5*girth)/(girth*.5))), 0, 100);
 128       return color((lx.getBaseHuef() + (360*(phase / TWO_PI)))%360, 80, b);
 129     }
 130   }
 131
 132   private final Helix h1;
 133   private final Helix h2;
 134
 135   private final BasicParameter helix1On = new BasicParameter("H1ON", 1);
 136   private final BasicParameter helix2On = new BasicParameter("H2ON", 1);
 137   private final BasicParameter basePairsOn = new BasicParameter("BPON", 1);
 138
 139   private static final float helixCoilPeriod = 100;
 140   private static final float helixCoilRadius = 45;
 141   private static final float helixCoilGirth = 20;
 142   private static final float helixCoilRotationPeriod = 10000;
 143
 144   private static final float spokePeriod = 40;
 145   private static final float spokeGirth = 10;
 146   private static final float spokePhase = 10;
 147   private static final float spokeRadius = 35; // helixCoilRadius - helixCoilGirth*.5f;
 148
 149   public HelixPattern(GLucose glucose) {
 150     super(glucose);
 151
 152     addParameter(helix1On);
 153     addParameter(helix2On);
 154     addParameter(basePairsOn);
 155
 156     PVector origin = new PVector(100, 50, 45);
 157     PVector axis = new PVector(1,0,0);
 158
 159     h1 = new Helix(
 160       new Line(origin, axis),
 161       helixCoilPeriod,
 162       helixCoilRadius,
 163       helixCoilGirth,
 164       0,
 165       helixCoilRotationPeriod);
 166     h2 = new Helix(
 167       new Line(origin, axis),
 168       helixCoilPeriod,
 169       helixCoilRadius,
 170       helixCoilGirth,
 171       PI,
 172       helixCoilRotationPeriod);
 173   }
 174
 175   private color calculateSpokeColor(final color h1c, final color h2c, final PVector pt) {
 176     // Find the closest spoke's t-value and calculate its
 177     // axis.  Until everything animates in the model reference
 178     // frame, this has to be calculated at every step because
 179     // the helices rotate.
 180     float t = h1.getAxis().getTValue(pt) + spokePhase;
 181     float spokeAxisTValue = floor(((t + spokePeriod/2) / spokePeriod)) * spokePeriod;
 182     PVector h1point = h1.pointOnToroidalAxis(spokeAxisTValue);
 183     // TODO(shaheen) investigate why h1.getAxis().getPointAt(spokeAxisTValue) doesn't quite
 184     // have the same value as finding the middle between h1point and h2point.
 185     PVector spokeCenter = h1.getAxis().getPointAt(spokeAxisTValue);
 186     PVector spokeVector = PVector.sub(h1point, spokeCenter);
 187     spokeVector.normalize();
 188     Line spokeLine = new Line(h1point, spokeVector);
 189     PVector pointOnSpoke = spokeLine.projectPoint(pt);
 190     float b = ((PVector.dist(pt, pointOnSpoke) < spokeGirth) && (PVector.dist(pointOnSpoke, spokeCenter) < spokeRadius)) ? 100.f : 0.f;
 191     return color(100, 80.f, b);
 192   }
 193
 194   void run(int deltaMs) {
 195     boolean h1on = helix1On.getValue() > 0.5;
 196     boolean h2on = helix2On.getValue() > 0.5;
 197     boolean spokesOn = (float)basePairsOn.getValue() > 0.5;
 198
 199     h1.step(deltaMs);
 200     h2.step(deltaMs);
 201
 202     for (Point p : model.points) {
 203       PVector pt = new PVector(p.x,p.y,p.z);
 204       color h1c = h1.colorOfPoint(pt);
 205       color h2c = h2.colorOfPoint(pt);
 206       color spokeColor = calculateSpokeColor(h1c, h2c, pt);
 207
 208       if (!h1on) {
 209         h1c = color(0,0,0);
 210       }
 211
 212       if (!h2on) {
 213         h2c = color(0,0,0);
 214       }
 215
 216       if (!spokesOn) {
 217         spokeColor = color(0,0,0);
 218       }
 219
 220       // The helices are positioned to not overlap.  If that changes,
 221       // a better blending formula is probably needed.
 222       colors[p.index] = blendColor(blendColor(h1c, h2c, ADD), spokeColor, ADD);
 223     }
 224   }
 225 }
 226