``````
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.

// Copyright 2007, Daniel Fontijne, University of Amsterdam -- fontijne@science.uva.nl

#ifdef WIN32
#include <windows.h>
#endif

#include <GL/gl.h>
#include <GL/glut.h>
#include <stdio.h>
#include <stdlib.h>

#include <string>

#include <libgasandbox/e3ga.h>
#include <libgasandbox/e3ga_draw.h>
#include <libgasandbox/e3ga_util.h>
#include <libgasandbox/gl_util.h>
#include <libgasandbox/glut_util.h>
#include <libgasandbox/timing.h>

using namespace e3ga;
using namespace mv_draw;

const char *WINDOW_TITLE = "Geometric Algebra, Chapter 10, Example 2: Crystallography";

// GLUT state information
int g_viewportWidth = 800;
int g_viewportHeight = 600;

// mouse position on last call to MouseButton() / MouseMotion()
e3ga::vector g_prevMousePos;

// when true, MouseMotion() will rotate the model
bool g_rotateModel = false;
bool g_rotateModelOutOfPlane = false;

// rotation of the model
rotor g_modelRotor(_rotor(1.0f));

// when dragging vectors: which one, and at what depth:
float g_dragDistance = -1.0f;
int g_dragObject = -1;

// the 7 crystal configurations
const int CUBIC = 1;
const int HEXAGONAL = 2;
const int TETRAGONAL = 3;
const int ORTHORHOMBRIC = 4;
const int TRICLINIC = 5;
const int MONOCLINIC = 6;
const int TRIGONAL = 7;

/*
These 3 vectors are used as input to generate the operators.
The user can drag them around, and they can also be set to
pre-programmed settings using the popup menu.
*/
const int NB_INPUT_VECTORS = 3;
e3ga::vector g_inputVectors[NB_INPUT_VECTORS] = {
_vector(e1),
_vector(e2),
_vector(e3)
};

// when either of these booleans is true, the operators are initialized in a special way
bool g_ac = false; // op 1 = a c, op 2 = b
bool g_abc = false; // op 1 = a b c

// the draggable point that is used as input for the `drawing the crystal'
e3ga::vector g_point = _vector(e1 + e2 + e3);

std::vector<mv> m_ops;

void recomputeOps() {
m_ops.clear();

// initialize array of operators:
std::vector<mv> &V = m_ops;
if (g_ac) {
V.push_back(g_inputVectors[0] ^ g_inputVectors[2]);
V.push_back(g_inputVectors[1]);
}
else if (g_abc) {
V.push_back(g_inputVectors[0] ^ g_inputVectors[1] ^ g_inputVectors[2]);
}
else {
for (int i = 0; i < NB_INPUT_VECTORS; i++)
V.push_back(g_inputVectors[i]);
}

// repeatedly apply every op to every op (very brute force)
double tStart = u_timeGet();
const double NB_VEC_LIMIT = 200; // limit on number of ops (48 is the actual limit, but we use 200 to visualize bad configurations)
while (V.size() < NB_VEC_LIMIT) {
unsigned int nbVec = (unsigned int)V.size();
for (unsigned int i = 0; i < nbVec; i++) {
for (unsigned int j = 0; j < nbVec; j++) {
mv v = V[j] * V[i];
bool newVersor = true;
for (unsigned int k = 0; k < V.size(); k++) {
const float CLOSE = 0.001f;
mv dif = v * inverse(V[k]);
if (_Float(norm_e(dif - _Float(dif))) < CLOSE) {
newVersor = false;
break;
}
}
if (newVersor) {
V.push_back(v);
if (V.size() == NB_VEC_LIMIT) {
i = j = nbVec;
break;
}
}
}
}
// stop when no new vectors have been discovered
if (nbVec == V.size()) break;
}
//  printf("%d operators\n", V.size());

}

void display() {
doIntelWarning(); // warn for possible problems with pciking on Intel graphics chipsets

// setup projection & transform for the vectors:
glViewport(0, 0, g_viewportWidth, g_viewportHeight);
glMatrixMode(GL_MODELVIEW);
glMatrixMode(GL_PROJECTION);
const float screenWidth = 1600.0f;
GLpick::g_frustumWidth = 2.0 *  (double)g_viewportWidth / screenWidth;
GLpick::g_frustumHeight = 2.0 *  (double)g_viewportHeight / screenWidth;
glFrustum(
-GLpick::g_frustumWidth / 2.0, GLpick::g_frustumWidth / 2.0,
-GLpick::g_frustumHeight / 2.0, GLpick::g_frustumHeight / 2.0,
GLpick::g_frustumNear, GLpick::g_frustumFar);
glMatrixMode(GL_MODELVIEW);
glTranslatef(0.0f, 0.0f, -8.0f);

glClearColor(1.0f, 1.0f, 1.0f, 1.0f);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

glDisable(GL_DEPTH_TEST);
glDisable(GL_LIGHTING);
glLineWidth(2.0f);

glMatrixMode(GL_MODELVIEW);
glPushMatrix();

rotorGLMult(g_modelRotor);

// draw the reflected points
if (!GLpick::g_pickActive) {
glColor3f(0.0f, 0.0f, 1.0f);
for (int i = 0; i < (int)m_ops.size(); i++) {
glBegin(GL_POINTS);
glEnd();
}
}

// draw the 3 input vectors
glColor3f(0.0f, 0.0f, 0.0f);
glLineWidth(3.0f);
for (unsigned int i = 0; i < NB_INPUT_VECTORS; i++) {
glBegin(GL_LINES);
glVertex3f(0.0f, 0.0f, 0.0f);
glVertex3fv(g_inputVectors[i].getC(vector_e1_e2_e3));
glEnd();
}

// draw the input points
glPointSize(5.0);
glColor3f(1.0f, 0.0f, 0.0f);
glBegin(GL_POINTS);
glVertex3fv(g_point.getC(vector_e1_e2_e3));
glEnd();

glPopMatrix();

if (!GLpick::g_pickActive) {
glViewport(0, 0, g_viewportWidth, g_viewportHeight);
glMatrixMode(GL_PROJECTION);
glOrtho(0, g_viewportWidth, 0, g_viewportHeight, -100.0, 100.0);
glMatrixMode(GL_MODELVIEW);

glDisable(GL_LIGHTING);
glColor3f(0.0f, 0.0f, 0.0f);
void *font = GLUT_BITMAP_HELVETICA_12;
renderBitmapString(20, 40, font, "Use the left mouse button to drag the red point and the black lines (or to orbit).");
renderBitmapString(20, 20, font, "Use the other mouse buttons to access the popup menu which contains pre-programmed configurations.");
}

if (!GLpick::g_pickActive) {
glutSwapBuffers();
}
}

void reshape(GLint width, GLint height) {
g_viewportWidth = width;
g_viewportHeight = height;

// redraw viewport
glutPostRedisplay();
}

e3ga::vector vectorAtDepth(double depth, const e3ga::vector &v2d) {
if ((GLpick::g_frustumWidth <= 0) || (GLpick::g_frustumHeight <= 0) ||
(GLpick::g_frustumNear <= 0) || (GLpick::g_frustumFar <= 0)) {
return e3ga::vector();
}

return _vector((depth * (double)v2d.e1() * GLpick::g_frustumWidth) / (g_viewportWidth * GLpick::g_frustumNear) * e1 +
(depth * (double)v2d.e2() * GLpick::g_frustumHeight) / (g_viewportHeight * GLpick::g_frustumNear) * e2);
}

e3ga::vector mousePosToVector(int x, int y) {
x -= g_viewportWidth / 2;
y -= g_viewportHeight / 2;
return e3ga::_vector((float)x * e1 - (float)y * e2);
}

void MouseButton(int button, int state, int x, int y) {
if (state == GLUT_UP) return;
g_rotateModel = false;
g_prevMousePos = mousePosToVector(x, y);
g_dragObject = pick(x, g_viewportHeight - y, display, &g_dragDistance);
//printf("Drag %d, %f\n", g_dragObject, g_dragDistance);
if (g_dragObject < 0) {
e3ga::vector mousePos = mousePosToVector(x, y);
g_rotateModel = true;
if ((_Float(norm_e(mousePos)) / _Float(norm_e(g_viewportWidth * e1 + g_viewportHeight * e2))) < 0.2)
g_rotateModelOutOfPlane = true;
else g_rotateModelOutOfPlane = false;
}
}

void MouseMotion(int x, int y) {
// get mouse position, motion
e3ga::vector mousePos = mousePosToVector(x, y);
e3ga::vector motion = _vector(mousePos - g_prevMousePos);
if (g_rotateModel) {
// update rotor
if (g_rotateModelOutOfPlane)
g_modelRotor = _rotor(e3ga::exp(0.005f * (motion ^ e3ga::e3)) * g_modelRotor);
else g_modelRotor = _rotor(e3ga::exp(0.00001f * (motion ^ mousePos)) * g_modelRotor);
}
else if (g_dragObject >= 0) {
e3ga::vector T = vectorAtDepth(g_dragDistance, motion);
T = _vector(inverse(g_modelRotor) * T * g_modelRotor);
if (g_dragObject == NB_INPUT_VECTORS) g_point += T;
else {
g_inputVectors[g_dragObject] += T;
recomputeOps();
}
}

// remember mouse pos for next motion:
g_prevMousePos = mousePos;

// redraw viewport
glutPostRedisplay();
}

g_ac = g_abc = false;
switch (value) {
case    CUBIC:
{
g_inputVectors[0] = _vector(e1);
g_inputVectors[1] = _vector(unit_e(e1 + e2));
g_inputVectors[2] = _vector(unit_e(e2 + e3));
}
break;
case HEXAGONAL:
{
g_inputVectors[0] = _vector(e1);
g_inputVectors[1] = _vector(e1 * exp(e1 ^ e2 * ((float)M_PI / 6.0f)));
g_inputVectors[2] = _vector(e3);
}
break;
case TETRAGONAL:
{
g_inputVectors[0] = _vector(e1);
g_inputVectors[1] = _vector(e1 * exp(e1 ^ e2 * ((float)M_PI / 4.0f)));
g_inputVectors[2] = _vector(e3);
}
break;
case ORTHORHOMBRIC:
{
g_inputVectors[0] = _vector(e1);
g_inputVectors[1] = _vector(e2);
g_inputVectors[2] = _vector(e3);
}
break;
case TRIGONAL:
{
g_ac = true;
g_inputVectors[0] = _vector(e1);
g_inputVectors[1] = _vector(g_inputVectors[0] * exp((e1^e2) * ((float)M_PI / 6.0f)));
g_inputVectors[2] = _vector(unit_e(e1 + e3));
}
break;
case MONOCLINIC:
{
g_ac = true;
g_inputVectors[0] = _vector(e1);
g_inputVectors[1] = _vector(e2);
g_inputVectors[2] = _vector(unit_e(e3 + 3.0f * e1));
}
break;
case TRICLINIC:
{
g_abc = true;
g_inputVectors[0] = _vector(e1);
g_inputVectors[1] = _vector(unit_e(e1 + e2 + e3));
g_inputVectors[2] = _vector(unit_e(e1 + -4.0f * e2));
}
break;

}
recomputeOps();

// redraw viewport
glutPostRedisplay();
}

int main(int argc, char*argv[]) {
// profiling for Gaigen 2:
e3ga::g2Profiling::init();

// GLUT Window Initialization:
glutInit (&argc, argv);
glutInitWindowSize(g_viewportWidth, g_viewportHeight);
glutInitDisplayMode( GLUT_RGB | GLUT_ALPHA | GLUT_DOUBLE | GLUT_DEPTH);
glutCreateWindow(WINDOW_TITLE);

// Register callbacks:
glutDisplayFunc(display);
glutReshapeFunc(reshape);
glutMouseFunc(MouseButton);
glutMotionFunc(MouseMotion);