Distance Tx, Ty according to Heading direction when you know the current point(x,y) - math note

Distance Tx, Ty according to Heading direction when you know the current point(x,y) - math note

Thank you~ ^^.

(TIP) Maple 15 - The method of the Matrix multiply (3by3 Rotation matrix)

(TIP) Maple 15 - The method of the Matrix multiply

Show the below example~

or
We can use LinearAlgebra command. Using 'with(LinearAlgebra)' keyword
Show next example~

Thank you~ ^^

(TIP) Maple 15 - the method of the matrix differential

(TIP) The method of the matrix differential in the Maple 15 math tool.
You should use "map" function. Show the below example.

Thanks you. ^^

Sample source to make SubWindow in the OpenGL/ glutCreateSubWindow / Multi Window

This sample source is the method to make subwindow in the openGL programming.

The source may apply to your problem, because I have tried to make easy.
(Source Download)

#include "glut.h"
#include 
#include 

using namespace std;


#define GAP  25             /* gap between subwindows */
GLuint window, View1, View2, View3, View4;
GLuint sub_width = 256, sub_height = 256;

void main_display(void);
void main_reshape(int width,  int height);
void setfont(char* name, int size);
void drawstr(GLuint x, GLuint y, const char* format, int length);
GLvoid *font_style = GLUT_BITMAP_TIMES_ROMAN_10;

void View1Display();
void View2Display();
void View3Display();
void View4Display();

void ResetViewport();

int main()
{
    //Mode Setting
    glutInitDisplayMode(GLUT_RGB | GLUT_DEPTH | GLUT_DOUBLE);
    //window size (+gap size)
    glutInitWindowSize(512+GAP*3, 512+GAP*3);
    //Initial position
    glutInitWindowPosition(50, 50);    

    //Main Window 
    window = glutCreateWindow("ViewPort Test");
    //Main Window callback function
    glutReshapeFunc(main_reshape);
    glutDisplayFunc(main_display);
    
    //World Window and Display
    View1 = glutCreateSubWindow(window, GAP, GAP, 256, 256);    
    glutDisplayFunc(View1Display);

    //screen Window and Display
    View2 = glutCreateSubWindow(window, GAP+256+GAP, GAP, 256, 256);
    glutDisplayFunc(View2Display);

    //command Window and Display
    View3 = glutCreateSubWindow(window, GAP+256+GAP, GAP+256+GAP, 256, 256);
    glutDisplayFunc(View3Display);

    View4 = glutCreateSubWindow(window, GAP+256+GAP, GAP+256+GAP, 256, 256);
    glutDisplayFunc(View4Display);


    glutMainLoop();

    return 0;
}

void main_display(void)
{
    //Background Color
    glClearColor(0.8, 0.8, 0.8, 0.0);
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

    //font color and style
    glColor3ub(0, 0, 0);
    setfont("helvetica", 12);

    //1st window name
    string str = "View1";
    drawstr(GAP, GAP-5, str.c_str(), str.length());

    //2st window name
    str = "View2";
    drawstr(GAP+sub_width+GAP, GAP-5, str.c_str(), str.length());

    //3st widnow name
    str = "View3";
    drawstr(GAP, GAP+sub_height+GAP-5, str.c_str(), str.length());

    //4st widnow name
    str = "View4";
    drawstr(GAP+sub_width+GAP, GAP+sub_height+GAP-5, str.c_str(), str.length());

    //last
    glutSwapBuffers();
}


//Background Window Setting
void main_reshape(int width,  int height) 
{
    //main view setting
    glViewport(0, 0, width, height);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluOrtho2D(0, width, height, 0);
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();

    sub_width = (width-GAP*3)/2.0;
    sub_height = (height-GAP*3)/2.0;

    //View1 Display
    glutSetWindow(View1);
    glutPositionWindow(GAP, GAP);
    glutReshapeWindow(sub_width, sub_height);

    //View2 Display
    glutSetWindow(View2);
    glutPositionWindow(GAP+sub_width+GAP, GAP);
    glutReshapeWindow(sub_width, sub_height);

    //View3 Display
    glutSetWindow(View3);
    glutPositionWindow(GAP, GAP+sub_height+GAP);
    glutReshapeWindow(sub_width, sub_height);


    //View4 Display
    glutSetWindow(View4);
    glutPositionWindow(GAP+sub_width+GAP, GAP+sub_height+GAP);
    glutReshapeWindow(sub_width, sub_height);
    //glutReshapeWindow(sub_width+GAP+sub_width, sub_height);    
}

//Font setting
void setfont(char* name, int size)
{
    font_style = GLUT_BITMAP_HELVETICA_10;
    if (strcmp(name, "helvetica") == 0) {
        if (size == 12) 
            font_style = GLUT_BITMAP_HELVETICA_12;
        else if (size == 18)
            font_style = GLUT_BITMAP_HELVETICA_18;
    } else if (strcmp(name, "times roman") == 0) {
        font_style = GLUT_BITMAP_TIMES_ROMAN_10;
        if (size == 24)
            font_style = GLUT_BITMAP_TIMES_ROMAN_24;
    } else if (strcmp(name, "8x13") == 0) {
        font_style = GLUT_BITMAP_8_BY_13;
    } else if (strcmp(name, "9x15") == 0) {
        font_style = GLUT_BITMAP_9_BY_15;
    }
}

//String Draw
void drawstr(GLuint x, GLuint y, const char* format, int length)
{
    glRasterPos2i(x, y);    
    for(int i=0; i        glutBitmapCharacter(font_style, *(format+i) );
}


//Display Teapot
void DrawScene()
{

    glColor3f(0.7, 0.7, 0.7);
    glPushMatrix();
    //glTranslatef(0.0, -1.0, 0.0);

    glBegin(GL_QUADS);
    glVertex3f(2.0, 0.0, 2.0);
    glVertex3f(2.0, 0.0, -2.0);
    glVertex3f(-2.0, 0.0, -2.0);
    glVertex3f(-2.0, 0.0, 2.0);
    glEnd();

    glPopMatrix();
    glColor3f(1.0, 1.0, 1.0);
    glPushMatrix();
    glTranslatef(0.0, 0.0, -0.5);
    glutWireTeapot(1.0);
    glPopMatrix();

}

//View1Display
void View1Display(){

    
    //viewport rest;
    ResetViewport();

    glClear(GL_COLOR_BUFFER_BIT);
    glColor3f(1.0, 1.0, 1.0);
    glPushMatrix();
    gluLookAt(0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);
    DrawScene();
    glPopMatrix();
    glutSwapBuffers();
}

//View2Display
void View2Display(){

    //viewport rest;
    ResetViewport();

    glClear(GL_COLOR_BUFFER_BIT);
    glColor3f(1.0, 1.0, 1.0);
    glPushMatrix();
    gluLookAt(1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);
    DrawScene();
    glPopMatrix();
    glutSwapBuffers();
}

//View3Display
void View3Display(){

    //viewport rest;
    ResetViewport();

    glClear(GL_COLOR_BUFFER_BIT);
    glColor3f(1.0, 1.0, 1.0);
    glPushMatrix();
    gluLookAt(0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0);
    DrawScene();
    glPopMatrix();
    glutSwapBuffers();
}


//View4Display
void View4Display(){

    //viewport rest;
    ResetViewport();

    glClear(GL_COLOR_BUFFER_BIT);
    glColor3f(1.0, 1.0, 1.0);
    glMatrixMode(GL_PROJECTION);
    glPushMatrix();
        glLoadIdentity();
        gluPerspective(30, 1.0, 3.0, 50.0);
        glMatrixMode(GL_MODELVIEW);
        glPushMatrix();
            gluLookAt(5.0, 5.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);
            DrawScene();
        glPopMatrix();
    glMatrixMode(GL_PROJECTION);
    glPopMatrix();
    glFlush();
    glutSwapBuffers();
}


void ResetViewport()
{
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    glOrtho(-2.0, 2.0, -2.0, 2.0, 0.5, 5.0);
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
}

(Tip) tbb.dll error

If you meet the the tbb.dll error message box when you compile the project including openCV library.
You can slove this problem.

Go to this web page
http://threadingbuildingblocks.org/ver.php?fid=174
Download latest version, and unzip.

Open the makefile.sin as Visual studio, the makefile.sin is located in the "build\vsproject". And Compile.
Then you can get tbb.dll file in the release folder.

This is my compiled tbb.dll file.
download tbb.dll


My environment is Visual Studio 2008, openCv 2.3, Window 7.

Thank you.

(Tip) Visual Studio Project Renamer Tool

Sometimes, we need to change the project name to other name.
Then this program is very useful.

Thank you.

Partial differential method of Composite function and multivariate (Chain Rule #1, #2)

Chain Rule #1.

EX) When there are equations,

How to calculate differential about t?

Chain Rule #2

 

 

EX)

Another example

This example might adapt a problem of the Image optimazation.

 

 

I hope this post help you.

Thank you.