one.empty3.library.ArcBall Maven / Gradle / Ivy
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3D rendering engine. Plus modeling. Expected glsl textures 3d and 2d rendering
/*
* Copyright (c) 2023. Manuel Daniel Dahmen
*
*
* Copyright 2012-2023 Manuel Daniel Dahmen
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package one.empty3.library;
import java.util.List;
import java.util.function.Consumer;
import java.util.logging.Level;
import java.util.logging.Logger;
/*__
* Created by manue on 03-11-19.
*/
public class ArcBall {
Representable representable;
public int glhProjectf(float objx, float objy, float objz, float[] modelview, float[] projection, int[] viewport, Point3D a) {
// Transformation vectors
float fTempo[] = new float[8];
// Modelview transform
fTempo[0] = modelview[0] * objx + modelview[4] * objy + modelview[8] * objz + modelview[12]; // w is always 1
fTempo[1] = modelview[1] * objx + modelview[5] * objy + modelview[9] * objz + modelview[13];
fTempo[2] = modelview[2] * objx + modelview[6] * objy + modelview[10] * objz + modelview[14];
fTempo[3] = modelview[3] * objx + modelview[7] * objy + modelview[11] * objz + modelview[15];
// Projection transform, the final row of projection matrix is always [0 0 -1 0]
// so we optimize for that.
fTempo[4] = projection[0] * fTempo[0] + projection[4] * fTempo[1] + projection[8] * fTempo[2] + projection[12] * fTempo[3];
fTempo[5] = projection[1] * fTempo[0] + projection[5] * fTempo[1] + projection[9] * fTempo[2] + projection[13] * fTempo[3];
fTempo[6] = projection[2] * fTempo[0] + projection[6] * fTempo[1] + projection[10] * fTempo[2] + projection[14] * fTempo[3];
fTempo[7] = -fTempo[2];
// The result normalizes between -1 and 1
if (fTempo[7] == 0.0) // The w value
return 0;
fTempo[7] = 1.0f / fTempo[7];
// Perspective division
fTempo[4] *= fTempo[7];
fTempo[5] *= fTempo[7];
fTempo[6] *= fTempo[7];
// Window coordinates
// Map x, y to range 0-1
a.set(0, (double) (fTempo[4] * 0.5f + 0.5f) * viewport[2] + viewport[0]);
a.set(1, (double) (fTempo[5] * 0.5f + 0.5f) * viewport[3] + viewport[1]);
// This is only correct when glDepthRange(0.0, 1.0)
a.set(2, (double) (1.0f + fTempo[6]) * 0.5f); // Between 0 and 1
return 1;
}
public int glhUnProjectf(float winx, float winy, float winz, float[] modelview, float[] projection, int[] viewport, float[] objectCoordinate) {
// Transformation matrices
float m[] = new float[16], A[] = new float[16];
float in[] = new float[4], out[] = new float[4];
// Calculation for inverting a matrix, compute projection x modelview
// and store in A[16]
MultiplyMatrices4by4OpenGL_FLOAT(A, projection, modelview);
// Now compute the inverse of matrix A
if (glhInvertMatrixf2(A, m) == 0)
return 0;
// Transformation of normalized coordinates between -1 and 1
in[0] = (winx - (float) viewport[0]) / (float) viewport[2] * 2.0f - 1.0f;
in[1] = (winy - (float) viewport[1]) / (float) viewport[3] * 2.0f - 1.0f;
in[2] = 2.0f * winz - 1.0f;
in[3] = 1.0f;
// Objects coordinates
MultiplyMatrixByVector4by4OpenGL_FLOAT(out, m, in);
if (out[3] == 0.0)
return 0;
out[3] = 1.0f / out[3];
objectCoordinate[0] = out[0] * out[3];
objectCoordinate[1] = out[1] * out[3];
objectCoordinate[2] = out[2] * out[3];
return 1;
}
public void MultiplyMatrices4by4OpenGL_FLOAT(float[] result, float[] matrix1, float[] matrix2) {
result[0] = matrix1[0] * matrix2[0] +
matrix1[4] * matrix2[1] +
matrix1[8] * matrix2[2] +
matrix1[12] * matrix2[3];
result[4] = matrix1[0] * matrix2[4] +
matrix1[4] * matrix2[5] +
matrix1[8] * matrix2[6] +
matrix1[12] * matrix2[7];
result[8] = matrix1[0] * matrix2[8] +
matrix1[4] * matrix2[9] +
matrix1[8] * matrix2[10] +
matrix1[12] * matrix2[11];
result[12] = matrix1[0] * matrix2[12] +
matrix1[4] * matrix2[13] +
matrix1[8] * matrix2[14] +
matrix1[12] * matrix2[15];
result[1] = matrix1[1] * matrix2[0] +
matrix1[5] * matrix2[1] +
matrix1[9] * matrix2[2] +
matrix1[13] * matrix2[3];
result[5] = matrix1[1] * matrix2[4] +
matrix1[5] * matrix2[5] +
matrix1[9] * matrix2[6] +
matrix1[13] * matrix2[7];
result[9] = matrix1[1] * matrix2[8] +
matrix1[5] * matrix2[9] +
matrix1[9] * matrix2[10] +
matrix1[13] * matrix2[11];
result[13] = matrix1[1] * matrix2[12] +
matrix1[5] * matrix2[13] +
matrix1[9] * matrix2[14] +
matrix1[13] * matrix2[15];
result[2] = matrix1[2] * matrix2[0] +
matrix1[6] * matrix2[1] +
matrix1[10] * matrix2[2] +
matrix1[14] * matrix2[3];
result[6] = matrix1[2] * matrix2[4] +
matrix1[6] * matrix2[5] +
matrix1[10] * matrix2[6] +
matrix1[14] * matrix2[7];
result[10] = matrix1[2] * matrix2[8] +
matrix1[6] * matrix2[9] +
matrix1[10] * matrix2[10] +
matrix1[14] * matrix2[11];
result[14] = matrix1[2] * matrix2[12] +
matrix1[6] * matrix2[13] +
matrix1[10] * matrix2[14] +
matrix1[14] * matrix2[15];
result[3] = matrix1[3] * matrix2[0] +
matrix1[7] * matrix2[1] +
matrix1[11] * matrix2[2] +
matrix1[15] * matrix2[3];
result[7] = matrix1[3] * matrix2[4] +
matrix1[7] * matrix2[5] +
matrix1[11] * matrix2[6] +
matrix1[15] * matrix2[7];
result[11] = matrix1[3] * matrix2[8] +
matrix1[7] * matrix2[9] +
matrix1[11] * matrix2[10] +
matrix1[15] * matrix2[11];
result[15] = matrix1[3] * matrix2[12] +
matrix1[7] * matrix2[13] +
matrix1[11] * matrix2[14] +
matrix1[15] * matrix2[15];
}
public void MultiplyMatrixByVector4by4OpenGL_FLOAT(float[] resultvector, float[] matrix, float[] pvector) {
resultvector[0] = matrix[0] * pvector[0] + matrix[4] * pvector[1] + matrix[8] * pvector[2] + matrix[12] * pvector[3];
resultvector[1] = matrix[1] * pvector[0] + matrix[5] * pvector[1] + matrix[9] * pvector[2] + matrix[13] * pvector[3];
resultvector[2] = matrix[2] * pvector[0] + matrix[6] * pvector[1] + matrix[10] * pvector[2] + matrix[14] * pvector[3];
resultvector[3] = matrix[3] * pvector[0] + matrix[7] * pvector[1] + matrix[11] * pvector[2] + matrix[15] * pvector[3];
}
public void SWAP_ROWS_DOUBLE(double[] a, double[] b) {
double[] _tmp = a;
(a) = (b);
(b) = _tmp;
}
public void SWAP_ROWS_FLOAT(float[] a, float[] b) {
float[] _tmp = a;
(a) = (b);
(b) = _tmp;
}
public float MAT0(float[] m, int r, int c) {
return (m)[(c) * 4 + (r)];
}
public void MAT(float[] m, int r, int c, float value) {
(m)[(c) * 4 + (r)] = value;
}
// This code comes directly from GLU except that it is for float
public int glhInvertMatrixf2(float[] m, float[] out) {
float wtmp[][] = new float[4][8];
float m0, m1, m2, m3, s;
float[] r0;
float[] r1;
float[] r2;
float[] r3;
r0 = wtmp[0];
r1 = wtmp[1];
r2 = wtmp[2];
r3 = wtmp[3];
r0[0] = MAT0(m, 0, 0);
r0[1] = MAT0(m, 0, 1);
r0[2] = MAT0(m, 0, 2);
r0[3] = MAT0(m, 0, 3);
r0[4] = 1.0f;
r0[5] = r0[6] = r0[7] = 0.0f;
r1[0] = MAT0(m, 1, 0);
r1[1] = MAT0(m, 1, 1);
r1[2] = MAT0(m, 1, 2);
r1[3] = MAT0(m, 1, 3);
r1[5] = 1.0f;
r1[4] = r1[6] = r1[7] = 0.0f;
r2[0] = MAT0(m, 2, 0);
r2[1] = MAT0(m, 2, 1);
r2[2] = MAT0(m, 2, 2);
r2[3] = MAT0(m, 2, 3);
r2[6] = 1.0f;
r2[4] = r2[5] = r2[7] = 0.0f;
r3[0] = MAT0(m, 3, 0);
r3[1] = MAT0(m, 3, 1);
r3[2] = MAT0(m, 3, 2);
r3[3] = MAT0(m, 3, 3);
r3[7] = 1.0f;
r3[4] = r3[5] = r3[6] = 0.0f;
/* choose pivot - or die */
if (Math.abs(r3[0]) > Math.abs(r2[0]))
SWAP_ROWS_FLOAT(r3, r2);
if (Math.abs(r2[0]) > Math.abs(r1[0]))
SWAP_ROWS_FLOAT(r2, r1);
if (Math.abs(r1[0]) > Math.abs(r0[0]))
SWAP_ROWS_FLOAT(r1, r0);
if (0.0 == r0[0])
return 0;
/* eliminate first variable */
m1 = r1[0] / r0[0];
m2 = r2[0] / r0[0];
m3 = r3[0] / r0[0];
s = r0[1];
r1[1] -= m1 * s;
r2[1] -= m2 * s;
r3[1] -= m3 * s;
s = r0[2];
r1[2] -= m1 * s;
r2[2] -= m2 * s;
r3[2] -= m3 * s;
s = r0[3];
r1[3] -= m1 * s;
r2[3] -= m2 * s;
r3[3] -= m3 * s;
s = r0[4];
if (s != 0.0) {
r1[4] -= m1 * s;
r2[4] -= m2 * s;
r3[4] -= m3 * s;
}
s = r0[5];
if (s != 0.0) {
r1[5] -= m1 * s;
r2[5] -= m2 * s;
r3[5] -= m3 * s;
}
s = r0[6];
if (s != 0.0) {
r1[6] -= m1 * s;
r2[6] -= m2 * s;
r3[6] -= m3 * s;
}
s = r0[7];
if (s != 0.0) {
r1[7] -= m1 * s;
r2[7] -= m2 * s;
r3[7] -= m3 * s;
}
/* choose pivot - or die */
if (Math.abs(r3[1]) > Math.abs(r2[1]))
SWAP_ROWS_FLOAT(r3, r2);
if (Math.abs(r2[1]) > Math.abs(r1[1]))
SWAP_ROWS_FLOAT(r2, r1);
if (0.0 == r1[1])
return 0;
/* eliminate second variable */
m2 = r2[1] / r1[1];
m3 = r3[1] / r1[1];
r2[2] -= m2 * r1[2];
r3[2] -= m3 * r1[2];
r2[3] -= m2 * r1[3];
r3[3] -= m3 * r1[3];
s = r1[4];
if (0.0 != s) {
r2[4] -= m2 * s;
r3[4] -= m3 * s;
}
s = r1[5];
if (0.0 != s) {
r2[5] -= m2 * s;
r3[5] -= m3 * s;
}
s = r1[6];
if (0.0 != s) {
r2[6] -= m2 * s;
r3[6] -= m3 * s;
}
s = r1[7];
if (0.0 != s) {
r2[7] -= m2 * s;
r3[7] -= m3 * s;
}
/* choose pivot - or die */
if (Math.abs(r3[2]) > Math.abs(r2[2]))
SWAP_ROWS_FLOAT(r3, r2);
if (0.0 == r2[2])
return 0;
/* eliminate third variable */
m3 = r3[2] / r2[2];
r3[3] -= m3 * r2[3];
r3[4] -= m3 * r2[4];
r3[5] -= m3 * r2[5];
r3[6] -= m3 * r2[6];
r3[7] -= m3 * r2[7];
/* last check */
if (0.0 == r3[3])
return 0;
s = 1.0f / r3[3]; /* now back substitute row 3 */
r3[4] *= s;
r3[5] *= s;
r3[6] *= s;
r3[7] *= s;
m2 = r2[3]; /* now back substitute row 2 */
s = 1.0f / r2[2];
r2[4] = s * (r2[4] - r3[4] * m2);
r2[5] = s * (r2[5] - r3[5] * m2);
r2[6] = s * (r2[6] - r3[6] * m2);
r2[7] = s * (r2[7] - r3[7] * m2);
m1 = r1[3];
r1[4] -= r3[4] * m1;
r1[5] -= r3[5] * m1;
r1[6] -= r3[6] * m1;
r1[7] -= r3[7] * m1;
m0 = r0[3];
r0[4] -= r3[4] * m0;
r0[5] -= r3[5] * m0;
r0[6] -= r3[6] * m0;
r0[7] -= r3[7] * m0;
m1 = r1[2]; /* now back substitute row 1 */
s = 1.0f / r1[1];
r1[4] = s * (r1[4] - r2[4] * m1);
r1[5] = s * (r1[5] - r2[5] * m1);
r1[6] = s * (r1[6] - r2[6] * m1);
r1[7] = s * (r1[7] - r2[7] * m1);
m0 = r0[2];
r0[4] -= r2[4] * m0;
r0[5] -= r2[5] * m0;
r0[6] -= r2[6] * m0;
r0[7] -= r2[7] * m0;
m0 = r0[1]; /* now back substitute row 0 */
s = 1.0f / r0[0];
r0[4] = s * (r0[4] - r1[4] * m0);
r0[5] = s * (r0[5] - r1[5] * m0);
r0[6] = s * (r0[6] - r1[6] * m0);
r0[7] = s * (r0[7] - r1[7] * m0);
MAT(out, 0, 0, r0[4]);
MAT(out, 0, 1, r0[5]);
MAT(out, 0, 2, r0[6]);
MAT(out, 0, 3, r0[7]);
MAT(out, 1, 0, r1[4]);
MAT(out, 1, 1, r1[5]);
MAT(out, 1, 2, r1[6]);
MAT(out, 1, 3, r1[7]);
MAT(out, 2, 0, r2[4]);
MAT(out, 2, 1, r2[5]);
MAT(out, 2, 2, r2[6]);
MAT(out, 2, 3, r2[7]);
MAT(out, 3, 0, r3[4]);
MAT(out, 3, 1, r3[5]);
MAT(out, 3, 2, r3[6]);
MAT(out, 3, 3, r3[7]);
return 1;
}
Double ab_quat[] = {1., 0., 0., 0., 0., 1., 0., 0., 0., 0., 1., 0., 0., 0., 0., 1.};
Double ab_last[] = {1., 0., 0., 0., 0., 1., 0., 0., 0., 0., 1., 0., 0., 0., 0., 1.};
Double ab_next[] = {1., 0., 0., 0., 0., 1., 0., 0., 0., 0., 1., 0., 0., 0., 0., 1.};
// the distance from the origin to the eye
Double ab_zoom = 1.0;
Double ab_zoom2 = 1.0;
// the radius of the arcball
Double ab_sphere = 10.0;
Double ab_sphere2 = 10.0;
// the distance from the origin of the plane that intersects
// the edge of the visible sphere (tangent to a ray from the eye)
Double ab_edge = 1.0;
// whether we are using a sphere or plane
Boolean ab_planar = false;
Double ab_planedist = 0.5;
Point3D ab_start = new Point3D(0., 0., 1.);
Point3D ab_curr = new Point3D(0., 0., 1.);
Point3D ab_eye = new Point3D(0., 0., 1.);
Point3D ab_eyedir = new Point3D(0., 0., 1.);
Point3D ab_up = new Point3D(0., 1., 0.);
Point3D ab_out = new Point3D(1., 0., 0.);
float ab_glp[] = {1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1};
float ab_glm[] = {1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1};
int ab_glv[] = {0, 0, 640, 480};
public void arcball_setzoom(double radius, Point3D eye, Point3D up) {
ab_eye = eye; // store eye vector
ab_zoom2 = ab_eye.prodScalaire(ab_eye);
ab_zoom = Math.sqrt(ab_zoom2); // store eye distance
ab_sphere = radius; // sphere radius
ab_sphere2 = ab_sphere * ab_sphere;
ab_eyedir = ab_eye.mult(1.0 / ab_zoom); // distance to eye
ab_edge = ab_sphere2 / ab_zoom; // plane of visible edge
if (ab_sphere <= 0.0) // trackball mode
{
ab_planar = true;
ab_up = up;
ab_out = (ab_eyedir.prodVect(ab_up));
ab_planedist = (0.0 - ab_sphere) * ab_zoom;
} else
ab_planar = false;
}
// convert the quaternion into a rotation matrix
public static void quaternion(Double[] q, Double x, Double y, Double z, Double w) {
Double x2 = x * x;
Double y2 = y * y;
Double z2 = z * z;
Double xy = x * y;
Double xz = x * z;
Double yz = y * z;
Double wx = w * x;
Double wy = w * y;
Double wz = w * z;
q[0] = 1 - 2 * y2 - 2 * z2;
q[1] = 2 * xy + 2 * wz;
q[2] = 2 * xz - 2 * wy;
q[4] = 2 * xy - 2 * wz;
q[5] = 1 - 2 * x2 - 2 * z2;
q[6] = 2 * yz + 2 * wx;
q[8] = 2 * xz + 2 * wy;
q[9] = 2 * yz - 2 * wx;
q[10] = 1 - 2 * x2 - 2 * y2;
}
// reset the rotation matrix
public static void quatidentity(Double[] q) {
q[0] = 1.;
q[1] = 0.;
q[2] = 0.;
q[3] = 0.;
q[4] = 0.;
q[5] = 1.;
q[6] = 0.;
q[7] = 0.;
q[8] = 0.;
q[9] = 0.;
q[10] = 1.;
q[11] = 0.;
q[12] = 0.;
q[13] = 0.;
q[14] = 0.;
q[15] = 1.;
}
// copy a rotation matrix
public static void quatcopy(Double[] dst, Double[] src) {
dst[0] = src[0];
dst[1] = src[1];
dst[2] = src[2];
dst[4] = src[4];
dst[5] = src[5];
dst[6] = src[6];
dst[8] = src[8];
dst[9] = src[9];
dst[10] = src[10];
}
// multiply two rotation matrices
public static void quatnext(Double[] dest, Double[] left, Double[] right) {
dest[0] = left[0] * right[0] + left[1] * right[4] + left[2] * right[8];
dest[1] = left[0] * right[1] + left[1] * right[5] + left[2] * right[9];
dest[2] = left[0] * right[2] + left[1] * right[6] + left[2] * right[10];
dest[4] = left[4] * right[0] + left[5] * right[4] + left[6] * right[8];
dest[5] = left[4] * right[1] + left[5] * right[5] + left[6] * right[9];
dest[6] = left[4] * right[2] + left[5] * right[6] + left[6] * right[10];
dest[8] = left[8] * right[0] + left[9] * right[4] + left[10] * right[8];
dest[9] = left[8] * right[1] + left[9] * right[5] + left[10] * right[9];
dest[10] = left[8] * right[2] + left[9] * right[6] + left[10] * right[10];
}
// find the intersection with the plane through the visible edge
public Point3D edge_coords(Point3D m) {
// find the intersection of the edge plane and the ray
Double t = (ab_edge - ab_zoom) / (ab_eyedir.prodScalaire(m));
Point3D a = ab_eye.plus(m.mult(t));
// find the direction of the eye-axis from that point
// along the edge plane
Point3D c = (ab_eyedir.mult(ab_edge).moins(a));
// find the intersection of the sphere with the ray going from
// the plane outside the sphere toward the eye-axis.
Double ac = a.prodScalaire(c);
Double c2 = (c.prodScalaire(c));
Double q = (0.0 - ac - Math.sqrt(ac * ac - c2 * ((a.prodScalaire(a) - ab_sphere2))) / c2);
return (a.plus(c.mult(q)).norme1());
}
// find the intersection with the sphere
public Point3D sphere_coords(float mx, float my) {
Point3D a = new Point3D();
gluUnProject(mx, my, 0, ab_glm, ab_glp, ab_glv, a);
Point3D m = a.moins(ab_eye);
// mouse position represents ray: eye + t*m
// intersecting with a sphere centered at the origin
Double a2 = m.prodScalaire(m);
Double b = (ab_eye.prodScalaire(m));
Double root = (b * b) - a2 * (ab_zoom2 - ab_sphere2);
if (root <= 0) return edge_coords(m);
Double t = (0.0 - b - Math.sqrt(root)) / a2;
return (ab_eye.plus((m.mult(t))).norme1());
}
// get intersection with plane for "trackball" style rotation
public Point3D planar_coords(float mx, float my) {
Point3D a = new Point3D();
gluUnProject(mx, my, 0, ab_glm, ab_glp, ab_glv, a);
Point3D m = a.moins(ab_eye);
// intersect the point with the trackball plane
Double t = (ab_planedist - ab_zoom) / (ab_eyedir.prodScalaire(m));
Point3D d = ab_eye.plus(m.mult(t));
return new Point3D(d.prodScalaire(ab_up), d.prodScalaire(ab_out), 0.0);
}
public int gluUnProject(float mx, float my, int mz, float[] ab_glm, float[] ab_glp, int[] ab_glv, Point3D a) {
float x = (float) (double) a.getX();
float y = (float) (double) a.getY();
float z = (float) (double) a.getZ();
float[] floats = {x, y, z};
int i = glhUnProjectf(mx, my, mz, ab_glm, ab_glp, ab_glv, floats);
a.set(0, (double) floats[0]);
a.set(1, (double) floats[1]);
a.set(2, (double) floats[2]);
return i;
}
// reset the arcball
public void arcball_init(Representable representable) {
this.representable = representable;
if(representable!=null) {
List d = representable.getRotation().getElem().getRot().getElem().getD().data1d;
int size = d.size();
Logger.getAnonymousLogger().log(Level.INFO, "List size rot = " + size);
Double[] a = new Double[12];
int[] i = new int[]{0};
d.forEach(new Consumer() {
@Override
public void accept(Double aDouble) {
a[i[0]] = aDouble;
i[0]++;
}
});
if (size == 9) {
a[9] = 0.0;
a[10] = 0.0;
a[11] = 1.0;
}
quatcopy(ab_quat, a);
}
}
// reset the arcball
public void arcball_reset(Representable representable) {
if(representable!=null) {
arcball_init(representable);
quatidentity(ab_quat);
quatidentity(ab_last);
}
}
// begin arcball rotation
public void arcball_start(int mx, int my) {
if(representable!=null) {
// saves a copy of the current rotation for comparison
quatcopy(ab_last, ab_quat);
if (ab_planar) ab_start = planar_coords(mx, my);
else ab_start = sphere_coords(mx, my);
}
}
// update current arcball rotation
public void arcball_move(int mx, int my) {
if (ab_planar) {
ab_curr = planar_coords(mx, my);
if (ab_curr.equals(ab_start)) return;
// d is motion since the last position
Point3D d = ab_curr.moins(ab_start);
Double angle = 3 * 0.5;
Double cosa = Math.cos(angle);
Double sina = Math.sin(angle);
// p is perpendicular to d
Point3D p = ((ab_out.mult(d.getX())).moins(ab_up.mult(d.getY()))).norme1().mult(sina);
quaternion(ab_next, p.getX(), p.getY(), p.getZ(), cosa);
quatnext(ab_quat, ab_last, ab_next);
// planar style only ever relates to the last point
quatcopy(ab_last, ab_quat);
ab_start = ab_curr;
} else {
ab_curr = sphere_coords(mx, my);
if (ab_curr.equals(ab_start)) { // avoid potential rare divide by tiny
quatcopy(ab_quat, ab_last);
return;
}
// use a dot product to get the angle between them
// use a cross product to get the vector to rotate around
Double cos2a = ab_start.prodScalaire(ab_curr);
Double sina = Math.sqrt((1.0 - cos2a) * 0.5);
Double cosa = Math.sqrt((1.0 + cos2a) * 0.5);
Point3D cross = (ab_start.prodVect(ab_curr)).norme1().mult(sina);
quaternion(ab_next, cross.getX(), cross.getY(), cross.getZ(), cosa);
// update the rotation matrix
quatnext(ab_quat, ab_last, ab_next);
ab_start = ab_curr;
}
representable.getRotation().getElem().getRot().getElem().setD(ab_last);
}
}