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

using namespace e3ga;
using namespace mv_draw;

const char *WINDOW_TITLE = "Geometric Algebra, Chapter 5, Example 1: Meet & Join";

// 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
e3ga::rotor g_modelRotor(_rotor(1.0f));

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

const int g_nbVectors = 3;

// the multivectors (initially set to bivectors)
mv g_M1 = e1 ^ e2;
mv g_M2 = unit_e((e1 + e3) ^ e2);

// what to draw:
#define DRAW_JOIN 1
#define DRAW_MEET 2
int g_draw = DRAW_MEET;

// returns 'c', rounded to multiples of 'M'
inline float round(float c, float M) {
c = c / M;
return (float)((c < 0) ? (int)(c - 0.5f) : (int)(c + 0.5f)) * M;
}

// rounds coordinates of 'X' to multiples of 'M'
mv round(const mv &X, float M) {
// ugly hack, making use of internals of Gaigen 2:
float R[8];
int s = mv_size[X.gu()];
for (int i = 0; i < s; i++) {
R[i] = round(X.m_c[i], M);
}
return mv(X.gu(), R);
}

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, -6.0f);

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

glEnable(GL_DEPTH_TEST);
glPolygonMode(GL_FRONT_AND_BACK, GL_FILL);
glEnable(GL_CULL_FACE);
glCullFace(GL_BACK);
glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0);
glLineWidth(2.0f);

glMatrixMode(GL_MODELVIEW);
glPushMatrix();

rotorGLMult(g_modelRotor);

mv M1 = g_M1;
mv M2 = g_M2;

// 'Round' the coordinates, to get a step-wise motion of the bivectors:
// This simplifies manipulating the bivectors such that they are equal.
M1 = unit_e(round(M1, 0.2f));
M2 = unit_e(round(M2, 0.2f));

g_drawState.pushDrawModeOff(OD_ORIENTATION);

// red: multivector 1
glColor3fm(1.0f, 0.0f, 0.0f);
draw(M1);

// green: multivector 2
glColor3fm(0.0f, 1.0f, 0.0f);
draw(M2);

// translate a bit (to prevent depth buffer artifacts)
glTranslatef(0.0f, 0.0f, 0.01f);

// draw the meet / join, in blue
try {
glEnable(GL_CULL_FACE);
glCullFace(GL_BACK);
if (!GLpick::g_pickActive) {
mv X;
if (g_draw == DRAW_MEET) X = meet(M1, M2);
else X = join(M1, M2);

// a little hack to draw everthing in the 'right' size:
double scale = 1.2f;
if (X.e1e2e3() != 0.0) scale = 0.5f;

glColor3fm(0.0f, 0.0f, 1.0f);
X = scale * unit_e(X);
draw(X);
}
} catch(std::string &str) {
printf("%s!\n", str.c_str());
}
g_drawState.popDrawMode();

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 left mouse button to rotate the red and green multivectors and to orbit scene");
renderBitmapString(20, 20, font, "-use other mouse buttons to access popup menu");

char buf[1024];
sprintf(buf, "The %s(red multivector, green multivector) is drawn in blue", (g_draw == DRAW_MEET) ? "meet" : "join");
//renderBitmapString(20, g_viewportHeight - 20, font, buf);

}

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 * e3ga::e1 - (float)y * e3ga::e2);
}

void MouseButton(int button, int state, int x, int y) {
g_rotateModel = false;

g_prevMousePos = mousePosToVector(x, y);

GLpick::g_pickWinSize = 1;
g_dragObject = pick(x, g_viewportHeight - y, display, &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 >= 1) && (g_dragObject <= 2)) {
//rotor R = _rotor(inverse(g_modelRotor) * e3ga::exp(0.005f * (motion ^ e3ga::e3)) * g_modelRotor);
rotor R = _rotor(inverse(g_modelRotor) * e3ga::exp(0.00005f * (motion ^ mousePos)) * g_modelRotor);
if (g_dragObject == 1) {
g_M1 = largestGradePart(R * g_M1 * inverse(R));
}
else if (g_dragObject == 2) {
g_M2 = largestGradePart(R * g_M2 * inverse(R));
}
}

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

// redraw viewport
glutPostRedisplay();

}

if ((value >= 1) && (value <= 3)) {
}
else if ((value >= 1 + 4) && (value <= 3 + 4)) {
}
else if (value == 10) {
g_draw = DRAW_MEET;
}
else if (value == 11) {
g_draw = DRAW_JOIN;
}

glutPostRedisplay();
}

void testMeetJoin() {
/*
for (int i = 0; i < 100000; i++) {

//      printf("\n%s\n", X.c_str());
printf("%s\n", (X - Y).c_str_e());
printf("%s\n", (X - Z).c_str_e());

}*/

/*
for (int i = 0; i < 100000; i++) {
mv Z = deltaProduct(X, Y, 1e-7f, &gradeIdxZ);
}*/
/*
for (int i = 0; i < 1000000; i++) {
X = unit_e(X);
Y = unit_e(Y);
mv M, J;
try {
meetJoin(X, Y, M, J);
} catch(std::string &str) {
printf("Error with the following:\n");
printf("%s\n", X.c_str_e());
printf("%s\n", Y.c_str_e());
//meetJoin(X, Y, M, J);
}
M = unit_e(M);
J = unit_e(J);
if (_Float(norm_e2(X << J)) < 0.5f)
printf("Ah 1!\n");
if (_Float(norm_e2(Y << J)) < 0.5f)
printf("Ah 2!\n");

if (_Float(norm_e2(M << X)) < 0.5f)
printf("Ah 3!\n");
if (_Float(norm_e2(M << Y)) < 0.5f)
printf("Ah 4!\n");
}
*/

}

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);