/**
* Input W must be initialized to a nonzero vector, output is {U,V,W}, an orthonormal basis. A
* hint is provided about whether or not W is already unit length.
*
* @param kU DOCUMENT ME!
* @param kV DOCUMENT ME!
* @param kW DOCUMENT ME!
* @param bUnitLengthW DOCUMENT ME!
*/
static void generateOrthonormalBasis(
MjVector3f kU, MjVector3f kV, MjVector3f kW, boolean bUnitLengthW) {
if (!bUnitLengthW) {
kW.normalizeSafe();
}
float fInvLength;
if (Math.abs(kW.x) >= Math.abs(kW.y)) {
// W.x or W.z is the largest magnitude component, swap them
fInvLength = 1.0f / (float) Math.sqrt((kW.x * kW.x) + (kW.z * kW.z));
kU.x = -kW.z * fInvLength;
kU.y = 0.0f;
kU.z = +kW.x * fInvLength;
} else {
// W.y or W.z is the largest magnitude component, swap them
fInvLength = 1.0f / (float) Math.sqrt((kW.y * kW.y) + (kW.z * kW.z));
kU.x = 0.0f;
kU.y = +kW.z * fInvLength;
kU.z = -kW.y * fInvLength;
}
kV.cross(kW, kU);
}
public class Tetrahedron extends Shape3D {
private static final float sqrt3 = (float) Math.sqrt(3.0);
private static final float sqrt3_3 = sqrt3 / 3.0f;
private static final float sqrt24_3 = (float) Math.sqrt(24.0) / 3.0f;
private static final float ycenter = 0.5f * sqrt24_3;
private static final float zcenter = -sqrt3_3;
private static final Point3f p1 = new Point3f(-1.0f, -ycenter, -zcenter);
private static final Point3f p2 = new Point3f(1.0f, -ycenter, -zcenter);
private static final Point3f p3 = new Point3f(0.0f, -ycenter, -sqrt3 - zcenter);
private static final Point3f p4 = new Point3f(0.0f, sqrt24_3 - ycenter, 0.0f);
private static final Point3f[] verts = {
p1, p2, p4, // front face
p1, p4, p3, // left, back face
p2, p3, p4, // right, back face
p1, p3, p2, // bottom face
};
private Point2f texCoord[] = {
new Point2f(0.0f, 0.0f), new Point2f(1.0f, 0.0f), new Point2f(0.5f, sqrt3 / 2.0f),
};
public Tetrahedron() {
int i;
TriangleArray tetra =
new TriangleArray(
12,
TriangleArray.COORDINATES | TriangleArray.NORMALS | TriangleArray.TEXTURE_COORDINATE_2);
tetra.setCoordinates(0, verts);
for (i = 0; i < 12; i++) {
tetra.setTextureCoordinate(i, texCoord[i % 3]);
}
int face;
Vector3f normal = new Vector3f();
Vector3f v1 = new Vector3f();
Vector3f v2 = new Vector3f();
Point3f[] pts = new Point3f[3];
for (i = 0; i < 3; i++) pts[i] = new Point3f();
for (face = 0; face < 4; face++) {
tetra.getCoordinates(face * 3, pts);
v1.sub(pts[1], pts[0]);
v2.sub(pts[2], pts[0]);
normal.cross(v1, v2);
normal.normalize();
for (i = 0; i < 3; i++) {
tetra.setNormal((face * 3 + i), normal);
}
}
this.setGeometry(tetra);
this.setAppearance(new Appearance());
}
}
/**
* Calculates the min and max boundaries of the structure after it has been transformed into its
* canonical orientation.
*/
private void calcBoundaries() {
minBoundary.x = Double.MAX_VALUE;
maxBoundary.x = Double.MIN_VALUE;
minBoundary.y = Double.MAX_VALUE;
maxBoundary.x = Double.MIN_VALUE;
minBoundary.z = Double.MAX_VALUE;
maxBoundary.z = Double.MIN_VALUE;
xzRadiusMax = Double.MIN_VALUE;
Point3d probe = new Point3d();
for (Point3d[] list : subunits.getTraces()) {
for (Point3d p : list) {
probe.set(p);
transformationMatrix.transform(probe);
minBoundary.x = Math.min(minBoundary.x, probe.x);
maxBoundary.x = Math.max(maxBoundary.x, probe.x);
minBoundary.y = Math.min(minBoundary.y, probe.y);
maxBoundary.y = Math.max(maxBoundary.y, probe.y);
minBoundary.z = Math.min(minBoundary.z, probe.z);
maxBoundary.z = Math.max(maxBoundary.z, probe.z);
xzRadiusMax = Math.max(xzRadiusMax, Math.sqrt(probe.x * probe.x + probe.z * probe.z));
}
}
// System.out.println("MinBoundary: " + minBoundary);
// System.out.println("MaxBoundary: " + maxBoundary);
// System.out.println("zxRadius: " + xzRadiusMax);
}
/**
* Return a midpoint of a helix, calculated from three positions of three adjacent subunit
* centers.
*
* @param p1 center of first subunit
* @param p2 center of second subunit
* @param p3 center of third subunit
* @return midpoint of helix
*/
private Point3d getMidPoint(Point3d p1, Point3d p2, Point3d p3) {
Vector3d v1 = new Vector3d();
v1.sub(p1, p2);
Vector3d v2 = new Vector3d();
v2.sub(p3, p2);
Vector3d v3 = new Vector3d();
v3.add(v1);
v3.add(v2);
v3.normalize();
// calculat the total distance between to subunits
double dTotal = v1.length();
// calculate the rise along the y-axis. The helix axis is aligned with y-axis,
// therfore, the rise between subunits is the y-distance
double rise = p2.y - p1.y;
// use phythagorean theoremm to calculate chord length between two subunit centers
double chord = Math.sqrt(dTotal * dTotal - rise * rise);
// System.out.println("Chord d: " + dTotal + " rise: " + rise + "chord: " + chord);
double angle = helixLayers.getByLargestContacts().getAxisAngle().angle;
// using the axis angle and the chord length, we can calculate the radius of the helix
// http://en.wikipedia.org/wiki/Chord_%28geometry%29
double radius = chord / Math.sin(angle / 2) / 2; // can this go to zero?
// System.out.println("Radius: " + radius);
// project the radius onto the vector that points toward the helix axis
v3.scale(radius);
v3.add(p2);
// System.out.println("Angle: " +
// Math.toDegrees(helixLayers.getByLowestAngle().getAxisAngle().angle));
Point3d cor = new Point3d(v3);
return cor;
}
/**
* Normalize this vector in place. If the vector is very close to zero length, then this vector is
* stored as the zero vector.
*/
void normalizeSafe() {
float fLengthSquared = lengthSquared();
if (0.0f == fLengthSquared) {
set(ZERO);
} else {
scale(1.0f / (float) Math.sqrt(fLengthSquared));
}
}
/**
* calculates z and adjusts for border conditions
*
* @param x
* @param y
* @return
*/
private float calculateZ(float x, float y) {
float z = 0;
z = 1 - x * x - y * y;
if (z > 0) {
z = (float) Math.sqrt(z);
} else {
z = 0;
}
return z;
}
public void vec2FieldMagnitude(Field field, AffineTransform ftoi) {
AffineTransform itof = null;
try {
itof = ftoi.createInverse();
} catch (NoninvertibleTransformException niv) {
TDebug.println(0, "NoninvertibleTransformException: " + niv);
}
Vector3d v = new Vector3d();
Point2D.Double p = new Point2D.Double();
for (int j = 0, k = 0; j < height; ++j)
for (int i = 0; i < width; ++i, ++k) {
p.x = i;
p.y = j;
itof.transform(p, p);
v = field.get(p.x, p.y, 0.0);
f[k] = (float) Math.sqrt(v.x * v.x + v.y * v.y);
}
}
boolean intersect(Ray r, Hit h, Range range) {
// ToDo:
boolean retVal = false;
double Aq = r.getDirection().dot(r.getDirection());
double Bq =
2
* r.getDirection()
.dot(
new Vector3d(
r.getOrigin().x - center.x,
r.getOrigin().y - center.y,
r.getOrigin().z - center.z));
double Cq =
(Math.pow(r.getOrigin().x - center.x, 2)
+ Math.pow(r.getOrigin().y - center.y, 2)
+ Math.pow(r.getOrigin().z - center.z, 2))
- Math.pow(radius, 2);
double discriminant = Math.pow(Bq, 2) - (4 * Aq * Cq);
// Hay intersección, si se cumple esta condición... solo se ne
// necesita el primer valor que es el de la primera intersección
if (discriminant >= 0) {
discriminant = Math.sqrt(discriminant);
double firstT = (-Bq - discriminant) / (2 * Aq);
if (firstT > range.minT && firstT < range.maxT) {
h.setColor(this.color);
range.maxT = firstT;
h.setT(firstT);
// se debe retornar T
}
retVal = true;
}
return retVal;
// Compute the intersection of the ray with the
// Sphere and update what needs to be updated
// Valid values for t must be within the "range"
// ...
}