## Plotting 4D Graphs With QOpenGLWidget

A 4D graph can be used for plotting a graph of a complex function, with complex numbers as its input and output. A complex number can be represented as a pair of two real numbers:

• A real part and an imaginary part.
• A magnitude and an argument.

An image has a width and a height, but you can add an illusion of depth using a linear transform and changes in hue. A common way to add the fourth dimension is to use colors to represent its value. If you use a color for the fourth dimension, you want to add a legend to tell the viewer how to estimate the value of the fourth coordinate.

A good example of one such graph is the graph of the Lambert function found in the Wikipedia.

The Lambert W function is defined as follows:

$x=ye^y\Rightarrow y=W_n(x)$

where $n \in \mathbb{Z}$ is the branch number.

In this post, I will discuss the use of Qt5 modules in creating my version of the graph:

The graph is not perfect and complete, but in this post I will explain how to create the components of the graph.

## Combining OpenGL and 2D Painting

In Qt5, the OpenGL widget is a painting device like any other widget. So, you can use a painter of class QPainter to paint 2D shapes on it. The painter is useful if you want to add text to an image. Remember to unbind every GL object (vertex array objects, buffers, textures) before painting with the painter.

Before painting with the GL functions, call the painter’s method beginNativePainting. After finishing the use of GL functions, call endNativePainting

If you want the text rotation, you can use SVG. A simple way to add SVG text is using the QSvgRenderer class, that can create an SVG image from a file or a string.

## Single Points

You can draw single points in OpenGL. To do so, you must enable GL_PROGRAM_POINT_SIZE using glEnable in your calling program, and define glPointSize in the vertex shader.

## Matrices

The main types of matrices used in my example are:

• Frustum – A perspective matrix defined using the minimum and maximum values of coordinates.
• Viewport – a matrix that transforms the coordinates used by GL into the coordinates of the input rectangle. That transform will be used for placing the axis ticks snd texts.

## The Program

The main window is a Qt Widget, so

### The QMake File: qmake.pro:

The following definition will be used for creating the make file.

TARGET=executable
SOURCES=main.cpp
HEADERS=graph.h
HEADERS+=shaders.h
HEADERS+=svg.h

DESTDIR=bin
QT=core
QT+=gui
QT+=svg

greaterThan(QT_MAJOR_VERSION, 4): QT+=widgets

### The main Header File

The header files ‘graph.h’ contains some definition to be used by the main program and the widget extending the QT Widget:

#include <QtWidgets/QOpenGLWidget>
#include <QOpenGLBuffer>
#include <QOpenGLVertexArrayObject>
#include <QOpenGLShader>
#include <QOpenGLShaderProgram>
#include <QOpenGLTexture>
#include <QPainter>
#include <QtSvg>
#include <QStyleOptionGraphicsItem>

struct graph_point {
GLfloat coords[3];
GLfloat hue;
};

struct vertex2D {
GLfloat coords[2];
GLfloat hue;
};

struct axis_ticks {
GLfloat rect_coords[3];
GLfloat texture_coords[2];
};

class GraphWidget:public QOpenGLWidget{
private:
QOpenGLVertexArrayObject m_vao;
QOpenGLBuffer m_gradient_vbo;
QOpenGLBuffer m_point_vbo;
QOpenGLBuffer m_ibo;

QOpenGLShader *m_vertexShader;
QOpenGLShader *m_fragmentShader;
QOpenGLShaderProgram *m_program;
QPainter m_painter;
QFont m_font;
int fontSize;
int m_width, m_height;
float legend_left;
QMatrix4x4 transform;
QMatrix4x4 viewport;

void addLegend(void);
void populatePointBuffer(void);
void paintGraph(void);
void draw3DLine(QVector4D fromVec, QVector4D toVec);
void addAxes(void);
void add_x_ticks(void);
void add_y_ticks(void);
void add_z_ticks(void);
void add_z_text(void);

public:
GraphWidget(QWidget *parent=nullptr);
~GraphWidget();
void initializeGL();
void paintGL();
void resizeGL(int w, int h);
};

### HSV to RGB

The fourth coordinate of our graph represents arg(W(z)), an angle. In the graph we’ll use HSV (Hue, Saturation, Value) because the hue is given by the value of an angle. A shader-language function to covert from HSV to RGB is defined in file “shaders.h“:

#define TO_RGB_FUNC					\
"#version 140\n"					\
"vec4 to_rgb(float hue){ \n"				\
"float s=1.0;\n"					\
"float v=1.0;\n"					\
"float c=v*s;\n"					\
"float   x=c*(1-abs(mod(3*hue,2)-1));\n"		\
"float   m=v-c;\n"					\
"vec3  tempRGB=hue< -2./3?  vec3(0,x,c):\n"		\
"              hue< -1./3?  vec3(x,0,c): \n"		\
"              hue<     0?  vec3(c,0,x): \n"		\
"              hue<  1./3?  vec3(c,x,0): \n"		\
"              hue<  2./3?  vec3(x,c,0): \n"		\
"		              vec3(0,c,x); \n"		\
"\n"							\
"return vec4(tempRGB+vec3(m,m,m),1);\n"		\
"}\n"

The shader fragment for both the graph points and the legend is defined as follows:

#define FRAGMENT_SHADER				\
TO_RGB_FUNC					\
"varying float f_hue;\n"			\
"void main(void){\n"				\
"    gl_FragColor=to_rgb(f_hue);\n"		\
"}\n"

### Main Program Includes and Definitions

#include <stdio.h>

#include <graph.h>
#include <QApplication>
#include "shaders.h"
#include "svg.h"
#include <complex>
#include <iostream>

#define MIN_WIDTH 640
#define MIN_HEIGHT 480

using namespace std;

### Constructor and Destructor

GraphWidget::GraphWidget(QWidget *parent):
QOpenGLWidget(parent),
m_vao(),
m_gradient_vbo(),
m_point_vbo(),
m_ibo(QOpenGLBuffer::IndexBuffer),
m_font()
{
setGeometry(0,0,MIN_WIDTH,MIN_HEIGHT);
setMinimumWidth(MIN_WIDTH);
setMinimumHeight(MIN_HEIGHT);
}

GraphWidget::~GraphWidget(){
makeCurrent();
m_point_vbo.destroy();
m_gradient_vbo.destroy();
m_ibo.destroy();
m_vao.destroy();
doneCurrent();

}

// NUM_ARGS - Args of complex numbers.
// NUM_MAGNS - Number of magnitudes.
#define NUM_ARGS 140
#define NUM_MAGNS 200

### Initializing, Populating the Point Buffer

Here we’ll define the variables that are initialize once. The following function, initializeGL, is called once upon the widget’s initization:

void GraphWidget::initializeGL(){
m_vertexShader=new QOpenGLShader(QOpenGLShader::Vertex);
m_fragmentShader=new QOpenGLShader(QOpenGLShader::Fragment);
makeCurrent();
glEnable(GL_BLEND);
glEnable(GL_DEPTH_TEST);
glEnable( GL_PROGRAM_POINT_SIZE );
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);

m_vao.create();

m_gradient_vbo.create();
m_gradient_vbo.bind();
m_gradient_vbo.allocate(4*sizeof(vertex2D));

m_point_vbo.create();
m_point_vbo.bind();
m_point_vbo.allocate(NUM_MAGNS*NUM_ARGS*sizeof(graph_point));
populatePointBuffer();

GLshort indices[6]={0,1,2,2,3,0};
m_ibo.create();
m_ibo.bind();
m_ibo.allocate(indices,sizeof(indices));
m_ibo.release();
m_gradient_vbo.release();
m_point_vbo.release();
m_program=new QOpenGLShaderProgram();
}

A call to glEnable( GL_PROGRAM_POINT_SIZE ); enables drawing single points.

The function populatePointBuffer uses the method ‘write‘ of class QOpenGLBuffer to write points to the vertex buffer. I use the buffer this way so I can use functions of complex variables.

void GraphWidget::populatePointBuffer(void){
int vboOffset=0;
graph_point vec[NUM_MAGNS];
for (float magn=0;magn<1.4;magn+=1.4/NUM_MAGNS){
int pos=0;
for (float arg=-1;arg<1;arg+=2./NUM_ARGS){
// The arg of W(Z) divided by pi.
complex<float> iarg;
iarg=complex<float>(0,M_PI*arg);
complex<float> w=magn*exp(iarg);
complex<float> z=w*exp(w);
vec[pos].hue=arg;
vec[pos].coords[0]=imag(z);
vec[pos].coords[1]=magn;
vec[pos].coords[2]=real(z);
pos+=1;
}
m_point_vbo.write(vboOffset,vec,sizeof(vec));
vboOffset+=sizeof(vec);
}
}

### Resizing

The function resizeGL is called as a response to a widget resize event. In this function the values that change due to a resize event are set. The properties set here are:

• The font size for the painter
• The transform matrix
• The viewport matrix
void GraphWidget::resizeGL(int w, int h){
m_width=w;
m_height=h;
fontSize=12.* min((float)m_width/MIN_WIDTH,(float)m_height/MIN_HEIGHT);
m_font.setPixelSize(fontSize);
float z_far=0.05;
float z_near=0.01;
float a=2./(m_height-2*fontSize);
float b=1.8-a*m_height;
float y_floor=b-2.*a*fontSize;

// leftInPixels,RightInPixels - left and right boundaries
//                              of the graph.
float leftInPixels=12*fontSize+7;
float rightInPixels=m_width - 12 - 15*fontSize;
a=2/(rightInPixels-leftInPixels);
b=-1-a*leftInPixels;
float x_left=b;
float x_right=a*m_width+b;

transform.setToIdentity();

transform.frustum(x_left,x_right,y_floor,1.8,z_near,z_far);
transform.translate(0,0,-(z_far+z_near)/2);
transform.scale(1,1,(z_far-z_near)/2);
viewport.setToIdentity();
viewport.viewport(rect());
}

### Painting

The function paintGL is called as a response to paint events. Following is the code of paintGL:

void GraphWidget::paintGL(){
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
m_painter.begin(this);
m_painter.setPen(QColor(255,255,255,255));
m_painter.setFont(m_font);
addLegend();
addAxes();

paintGraph();

m_painter.end();
}

Let us look at the functions called by the paint event handler:

#### Add Legend

The function addLegend uses OpenGL function to create the HSV gradient and the painter to add ticks and text values:

void GraphWidget::addLegend(void){
QString str="arg(W(Z))";

// Drawing the header

QRect boundingRect=m_painter.boundingRect(rect(),0,str);

m_painter.beginNativePainting();

m_vao.bind();
QMatrix4x4 mat;
mat.ortho(rect());
GLfloat top=boundingRect.height()+20;
GLfloat bottom=top+0.75*m_height;
GLfloat left=m_width-boundingRect.width()-10;
GLfloat right=left+0.25*boundingRect.width();
legend_left = left; // Add it to the private members.
vertex2D rect_vertices[4]={{{left,top},1},{{right,top},1},
{{right,bottom},-1},{{left,bottom},-1}};
m_gradient_vbo.bind();
m_ibo.bind();
GLshort indices[6]={0,1,2,2,3,0};
m_ibo.write(0,indices,sizeof(indices));
m_gradient_vbo.write(0,rect_vertices,sizeof(rect_vertices));

m_program->addShaderFromSourceCode(QOpenGLShader::Vertex,LEGEND_VERTEX_SHADER);
m_program->addShaderFromSourceCode(QOpenGLShader::Fragment,FRAGMENT_SHADER);
m_program->bind();
m_program->link();
m_program->setAttributeBuffer("legend_coords",
GL_FLOAT,
0,
2,
sizeof(vertex2D));
m_program->setAttributeBuffer("legend_hue",
GL_FLOAT,
sizeof(rect_vertices[0].coords),
1,
sizeof(vertex2D));
m_program->setUniformValue("ortho",mat);

m_vao.release();
m_vao.bind();
m_program->enableAttributeArray("legend_coords");
m_program->enableAttributeArray("legend_hue");
glDrawElements(GL_TRIANGLES,6,GL_UNSIGNED_SHORT,0);

m_vao.release();
m_program->disableAttributeArray("legend_coords");
m_program->disableAttributeArray("legend_hue");
m_program->release();
m_program->removeAllShaders();
m_gradient_vbo.release();
m_ibo.release();

m_painter.endNativePainting();
m_painter.drawText(m_width-boundingRect.width()-10,boundingRect.height()+10,str);

// Adding legend ticks
QString vals[7]={"pi","2pi/3","pi/3","0","-pi/3","-2pi/3","-pi"};
float curr_height=top;
float dist=(bottom-top)/6;
for (int i=0;i<7;i++){
m_painter.drawLine(right,curr_height,right+10,curr_height);
m_painter.drawText(right+15,curr_height+0.4*boundingRect.height(),vals[i]);
curr_height+=dist;
}
}

Following is the macro in shaders.h, which defines the vertex shader for the legend:

#define LEGEND_VERTEX_SHADER					\
"attribute vec2 legend_coords;\n"				\
"attribute float legend_hue;\n"				\
"uniform mat4 ortho;\n"					\
"varying float f_hue;\n"					\
"void main(void){\n"						\
"    gl_Position=ortho*vec4(legend_coords,0,1);\n"		\
"    f_hue=legend_hue;\n"					\
"}"

#### Add Axes

The function addAxes uses the painter and the viewport matrix to draw axes and add the ticks. You hove noticed that the matrices are of size 4×4 and the vectors are of length 4; when a matrix is multiplied by 4, you should divide coordinates x,y by coordinate w to find the vector’s location on the 2D window. Special treatment is added to the slanted z-axis, where SVG is used:

void GraphWidget::addAxes(void){

QVector4D startVec,endVec;

// Draw the x-axis
startVec=viewport*transform*QVector4D(-1,-0.2,1.1,1);
endVec=viewport*transform*QVector4D(1,-0.2,1.1,1);
draw3DLine(startVec,endVec);
add_x_ticks();

// Draw the y-axis
startVec=viewport*transform*QVector4D(-1,-0.2,1.1,1);
endVec=viewport*transform*QVector4D(-1,1.4,1.1,1);
draw3DLine(startVec,endVec);
add_y_ticks();

// Draw the z-axis
startVec=viewport*transform*QVector4D(1,-0.2,-1,1);
endVec=viewport*transform*QVector4D(1,-0.2,1.1,1);
draw3DLine(startVec,endVec);
add_z_ticks();
}

void GraphWidget::draw3DLine(QVector4D fromVec, QVector4D toVec){
m_painter.drawLine(fromVec.x()/fromVec.w(),
m_height-fromVec.y()/fromVec.w(),
toVec.x()/toVec.w(),
m_height-toVec.y()/toVec.w());
}

void GraphWidget::add_x_ticks(){
QVector4D start_point,end_point;
QString vals[]={"-1","-0.5","0","0.5","1"};
int i=0;
for (float loc=-1;loc<=1;loc+=0.5){
start_point=viewport*transform*QVector4D(loc,-0.2,1.1,1);
start_point.setX(start_point.x()/start_point.w());
start_point.setY(m_height-start_point.y()/start_point.w());
end_point=start_point;
end_point.setY(end_point.y()+5);
m_painter.drawLine(start_point.x(),start_point.y(), end_point.x(),end_point.y());
m_painter.drawText(start_point.x(),end_point.y()+fontSize+1,vals[i++]);
}
const char *text="Im(Z)";
QVector4D start_vector=viewport*transform*QVector4D(-1,-0.2,1.1,1);
QVector4D end_vector=viewport*transform*QVector4D(1,-0.2,1.1,1);
float text_start=(start_vector.x()+end_vector.x())/(2.*end_vector.w())-2*fontSize;
float bottom=m_height-end_vector.y()/end_vector.w()+2*fontSize+5;
m_painter.drawText(text_start,bottom,text);
}

void GraphWidget::add_y_ticks(){
QVector4D start_point,end_point;
QString vals[]={"0.0","0.2","0.4","0.6","0.8","1.0","1.2","1.4"};
int i=0;
for (float loc=0;loc<=1.41;loc+=0.2){
start_point=viewport*transform*QVector4D(-1,loc,1.1,1);
start_point.setX(start_point.x()/start_point.w());
start_point.setY(m_height-start_point.y()/start_point.w());
end_point=start_point;
end_point.setX(end_point.x()-5);
m_painter.drawLine(start_point.x(),start_point.y(), end_point.x(),end_point.y());
m_painter.drawText(end_point.x()-2*fontSize,end_point.y()+0.5*fontSize,vals[i++]);

}
const char *text="|W(z)|";
QVector4D start_vector=viewport*transform*QVector4D(-1,-0.2,1.1,1);
QVector4D end_vector=viewport*transform*QVector4D(1,1,1.1,1);
float text_y_position=(start_vector.y()+end_vector.y())/(2.*end_vector.w())-2*fontSize;
float text_rightmost=start_vector.x()/start_vector.w()-6*fontSize;
m_painter.drawText(text_rightmost,text_y_position,text);
}

void GraphWidget::add_z_ticks(){
QVector4D start_point,end_point;
QString vals[]={"-1","-0.5","0","0.5","1"};
int i=0;
for (float loc=-1;loc<=1;loc+=0.5){
start_point=viewport*transform*QVector4D(1,-0.2,loc,1);
start_point.setX(start_point.x()/start_point.w());
start_point.setY(m_height-start_point.y()/start_point.w());
end_point=start_point;
end_point.setY(end_point.y()-5);
m_painter.drawLine(start_point.x(),start_point.y(), end_point.x(),end_point.y());
if (i!=1){
m_painter.drawText(end_point.x()-fontSize/2.,end_point.y()-1,vals[i]);
}
i+=1;
}
add_z_text();
}

void GraphWidget::add_z_text(){
char *svg_str=(char *)calloc(strlen(SVG_TEXT_STR)+1,sizeof(char));
const char *text="Re(Z)";
QVector4D start_point,end_point;
start_point=viewport*transform*QVector4D(1,-0.2,1,1);
start_point.setX(start_point.x()/start_point.w());
start_point.setY(m_height-start_point.y()/start_point.w());
end_point=viewport*transform*QVector4D(1,-0.2,-1,1);
end_point.setX(end_point.x()/end_point.w());
end_point.setY(m_height-end_point.y()/end_point.w());
qreal inRadians=qAtan2(end_point.y()-start_point.y(),end_point.x()-start_point.x());
qreal inDegrees=qRadiansToDegrees(inRadians)+180;
float centerX=(start_point.x()+end_point.x())/2.;
float centerY=(start_point.y()+end_point.y())/2.;
float lenOfText=(strlen(text)-1.5)*fontSize;
float textX=centerX-lenOfText;
float textY=centerY+fontSize;

sprintf(svg_str,SVG_TEXT_STR,textX,textY,fontSize,inDegrees,centerX,centerY,text);
cout<<svg_str<<endl;
cout<<"Length of svg_str"<<strlen(svg_str)<<endl;
cout<<"Lenght of SVG_TEXT_STR"<<strlen(SVG_TEXT_STR)<<endl;

QSvgRenderer renderer((QByteArray(svg_str)));
renderer.render(&m_painter,rect());

}

The function add_z_text renders the SVG text using an object of call QSvgRendered. It accepts a byte array made from a string. It can also take a file name. The macro SVG_TEXT_STR is defined in file “svg.h” as follows:/code

#define SVG_TEXT_STR							\
"<svg>"								\
"    <text x='%.0f'" 							\
"          y='%.0f'"							\
"          font-size='%dpx'"						\
"          stroke='white'"						\
"          fill='white'"						\
"          transform='rotate(%.0f ,  %.0f ,  %.0f)'>%s</text>"	\
"</svg>"

#### Painting the Graph

Following is the function that paints the graph:

void GraphWidget::paintGraph(){
m_painter.beginNativePainting();
m_vao.bind();
m_point_vbo.bind();
m_program->addShaderFromSourceCode(QOpenGLShader::Vertex, GRAPH_VERTEX_SHADER);
m_program->addShaderFromSourceCode(QOpenGLShader::Fragment, FRAGMENT_SHADER);
m_program->bind();
m_program->link();
m_program->setAttributeBuffer("graph_coords",
GL_FLOAT,
0,
3,
sizeof(graph_point));
m_program->setAttributeBuffer("hue",
GL_FLOAT,
3*sizeof(GLfloat),
1,
sizeof(graph_point));
m_program->setUniformValue("transform",transform);
m_vao.release();
m_vao.bind();
m_program->enableAttributeArray("graph_coords");
m_program->enableAttributeArray("hue");
glDrawArrays(GL_POINTS,0,NUM_ARGS*NUM_MAGNS);
m_program->removeAllShaders();
m_program->release();
m_point_vbo.release();
m_vao.release();
m_painter.endNativePainting();
}

### The Main Function

Following is the code of the main function:

int main(int argc, char *argv[]){
QApplication app(argc, argv);
GraphWidget w;
w.show();

return app.exec();
}

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## OpenGL Made Simple with Qt5

Drawing and painting a 3D image with GL – the Graphic Library – is not as trivial as doing the same on a 2D canvas: no 3D versions of the 2D canvas drawing methods are defined in GL classes. Instead, programs written with GL send data to the GPU (Graphic Processing Unit), and directions for organizing the data in data structures and for the rendition of data to the screen. The data is stored in buffers, and processed by shader programs.

Once you know how to use the OpenGL API, drawing the following image is simple:

The way Qt simplifies the use of GL are as follows:

• it offers classes instead of integers to wrap GL resources: buffers, textures, vertex array and more.
• the classes include overloaded functions.
• the developer can create shaders without specifying the GL version.
• Qt manages the main loop.

The following sections will describe the process of painting a 3D surface.

## Initializing

To start working with GL, create an object of class QOpenGLWidget. Better create a subclass of QOpenGLWidget, if you work with Qt 5.4 or a later version. Don’t perform any GL operations before the method initializeGL is called. If you extend OpenGLWidget, any GL operation should be performed by one of the following methods: initializeGL, paintGL and resizeGL.

In initializeGL place operation to be performed once only at the initialization time. Some examples of initializeGL can be found in

Qt Assistnat->Qt Widgets->C++ Classes->QOpenGLWidget

click the code examples link.

Following is the initialization stage of my program to paint the triangle:

## The Class

Following is a definition of the ExtendedOpenGLWidget class:

#include <QtWidgets/QOpenGLWidget>
#include <QOpenGLVertexArrayObject>
#include <QOpenGLBuffer>
#include <QOpenGLShaderProgram>
#include <QOpenGLShader>
#include <QOpenGLContext>

class ExtendedOpenGLWidget:public QOpenGLWidget {
private:
QOpenGLVertexArrayObject m_vao;
QOpenGLBuffer m_vbo;
QOpenGLShaderProgram *m_program;
QOpenGLShader *m_fragmentShader, *m_vertexShader;
public:
ExtendedOpenGLWidget(QWidget *parent=nullptr);
~ExtendedOpenGLWidget();
void initializeGL();
void paintGL();
};

The class is defined in file “ui_opengl.h”.

### Include Headers

#include <ui_opengl.h>
#include <iostream>

using namespace std;

The file “ui_opengl” is the header file generated by th Qt Designer. The rest can be used for debug printing.

### The vertices

Vertices coordinates and colors are defined in my program as follows:

struct vertex {
float coords[3];
float colors[4];
};

struct vertex {
float coords[3];
float colors[4];
};
vertex vertices[]={
{{-0.9, -0.9, 0.0}, {0.0, 0.0, 1.0, 1.0}},
{{ 0.9, -0.9, 0.0}, {0.0, 1.0, 0.0, 1.0}},
{{ 0.0,  0.9, 0.0}, {1.0, 0.0, 0.0, 1.0}}
};

The above is a definition of a global variable. If you put it in a class, you will have to specify array sizes.

### Constructor

The only thing the constructor does is call the parent constructor:

ExtendedOpenGLWidget::ExtendedOpenGLWidget(QWidget *parent):QOpenGLWidget(parent){
}

### The initializeGL method

This function creates the vertex array object(VAO). If the VAO cannot be created, it cannot be bound to the context. Your program can draw with or without it. In my example, I bind the VAO.

What actually does the drawing is the shader program. For it to draw you should link it at run time with the shaders. If you use Qt 5, the class QOpenGLShaderProgram exists with a method addShaderFromSourceCode, so you can create program in separate text files without the need to recompile your GL program when the shader code changes.

The example in Qt Assistant->Qt GUI->C++ Classes->QOpenGLShaderProgram does not complete the example in Qt Assistnat->Qt Widgets->C++ Classes->QOpenGLWidget; Don’t use it if you bind a buffer, because the coordinates and colors defined by setAttributeArray and setUniformValue will not set the correct locations of the colors of coordinates for the drawing method. In addition, only use coordinates specified in pixel if the GL Widget is of fixed size.

Following is an initializeGL method for coordintes whose values are between -1 and 1, and the color RGBA values are floats between 0 and 1:

void ExtendedOpenGLWidget::initializeGL(){
glEnable(GL_BLEND);
glEnable(GL_DEPTH_TEST);
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
m_vao.create();
if (m_vao.isCreated()){
cout<<"Created"<<endl;
m_vao.bind();
}
m_vbo.create();
m_vbo.bind();

// Allocating buffer memory and populating it
m_vbo.allocate(vertices, sizeof(vertices));

m_fragmentShader=new QOpenGLShader(QOpenGLShader::Fragment);
m_fragmentShader->compileSourceFile("../fragmentshader.txt");
m_vertexShader=new QOpenGLShader(QOpenGLShader::Vertex);
m_vertexShader->compileSourceFile("../vertexshader.txt");
m_program=new QOpenGLShaderProgram();
m_program->addShader(m_fragmentShader);
m_program->addShader(m_vertexShader);
m_program->link();
m_program->bind();

// Arguments of setAttributeBuffer in this example:
//    1: A string, the corresponding attribute in the shaders.
//    2: the type of each array element.
//    3: the start point relative to the beginning of the current buffer.
//    4: the number of elements in each vector.
//    5: stride: the difference in bytes between two successive vectors
m_program->setAttributeBuffer("vertex", GL_FLOAT,0,3,sizeof(vertex));
m_program->setAttributeBuffer("color", GL_FLOAT,sizeof(vertices[0].coords),4,sizeof(vertex));
m_program->enableAttributeArray("vertex");
m_program->enableAttributeArray("color");
m_vao.release();
}

### Shaders

The program uses two shaders:

• a vertex shader – outputs the coordinates of which point
• a fragment shader – outputs the color of which point.
• Following are the files:

Vertex shader:

attribute highp vec3 vertex;
attribute highp vec4 color;
varying highp vec4 f_color;
void main(void){
gl_Position=vec4(vertex,1.0);
f_color=color;
}

Fragment shader:

varying mediump vec4 f_color;
void main(void){
gl_FragColor = f_color;
}

## Drawing

The method paintGL draws the image. In this example, it uses the function glDrawArrays with the mode GL_TRIANGLES. In 3D the only 3D polygon type a graphical program always knows how to fill because the vertices are on the same plan.

Following is the paintGL method:

void ExtendedOpenGLWidget::paintGL(){
cout<<"paint"<<endl;
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
m_vao.bind();
// Arguments of setAttributeBuffer in this example:
//    1. mode - how the shaders will draw the array
//    2. start - first enabled array
//    3. count - the number of indices.
glDrawArrays(GL_TRIANGLES,0,3);
m_vao.release();
}

## The main function

An Open GL Widget may be a top-level window or a widget inside another container. In the following main function, the widget is inside a main window:

int main(int argc, char *argv[]){
QApplication app(argc, argv);
QMainWindow mainWindow;
Ui_MainWindow mainObject;
mainObject.setupUi(&mainWindow);
mainWindow.show();
return app.exec();
}

## A Destructor

If you want to avoid warnings at the end of the execution, you better define a destructor to clean up the allocated objects.

Following is the code of one:

ExtendedOpenGLWidget::~ExtendedOpenGLWidget(){
makeCurrent();
m_vao.destroy();
m_vbo.destroy();
delete m_fragmentShader;
delete m_vertexShader;
delete m_program;
doneCurrent();
}

Learn more about OpenGL here

## Design and Develop GUI with Qt5

Qt allows you to develop a multi-platform application, that you can develop a GUI application on one platform and deploy to many others (if you avoid system-specific extra modules). Qt contains modules for creating widgets from elementary ones to OpenGL 3D, which I will discuss later. In addition it contains module with other functionalities an application may need such as SQL, XML, web channels, web views and web sockets.

Qt can be downloaded from https://www.qt.io/ or installed using the UNIX/Linux package installers.

In addition to the QT libraries and header files, there are 3 useful resources:

• Qt Designer – A GUI tool for the generation of Python and C++ headers from a form graphically designed.
• Qt Assistant – A reference to the Qt classes, Example, the QMake tutorial, etc.
• qmake – an easy-to-use utility that creates the Makefile.

In the following sections, I will show how to create a project using the three tools:

## Creating the Main Window

Qt Designer is an editor with which GUI designers and developers can communicate. With the designer you can create, save and edit Designer UI Files (*.ui) and create class files from them for Python and C++ programs. The QMake program discussed later can use the “.ui” file to generate a header file from it. The file can be edited by creating top level windows such as widows and dialog, and dragging and dropping widgets into them. You can also access and modify their properties; if you are a developer and have a Desiger UI file, you can find names of object in your program.

### Starting:

As you start the QT Designer, the following dialog pops up:

If you don’t see the dialog, choose File->New from the editor’s menu bar, to make the dialog pop up.

Choose your top-level widget from the “templates/forms” menu, and click Create; a window will be created:

Now, from the right-hand Property Editor, you can change some properties, for example: let us change the window title:

### Adding widgets and promoting them

Now, you can choose widgets from the left-hand side of the editors and drag-and-drop them into the window:

For example, let us add a push button, and change its QAbstractButton property “text” to “Push me!”.

One of the other properties we can change is the QObject property “objectName”, which will be the name of the appropriate field of class QPushButton in the created class.

By right-clicking inside the widget and choosing “Promote to..” from the context-menu, you can choose to use a class that inherits from the gadget’s class. Don’t forget to define the new class and its constructor and methods.

### Previewing

You can view your design by clicking Form->Preview from the editor’s menu bar.

### Saving the created class

If you don’t want the Make program to generate a header file, you can save it from the Qt Designer tool.

1. Choose Form->View C++ Vode/View Python Code from the editor’s menu bar.
a dialog will open.
2. Click the “save” icon to save the created header file.

## Adding Functionality

This section will describe a little Hello World program – in C++ – that uses a header file created wit QtDesigner. The purpose of the program is to print “Hello, world” to the standard output, when the “Push Me” button is clicked. To add the mouse event handling the class QPushButton has been promoted to Extended Button. This section will describe the program, and will help you train yourself using Qt Assistant.

### The main function

To learn what a the main function of a Qt Application with widgets should look like:

1. Start the Qt Assistant if not started yet.
2. Click the Contents tab
3. Click Qt Widgets (highlighted in the following image:

You” see a heading reading “Getting Started Programming with Qt Widgets”. Scroll down and see the contents of a main source line.

In the Hello World program the code is as follows:

#include "ui_example.h"
#include <iostream>

using namespace std;

ExtendedButton::ExtendedButton(QWidget *parent):QPushButton(parent) {
}
void ExtendedButton::mouseReleaseEvent(QMouseEvent *event){
cout<<"Hello, world!"<<endl;
}
int main(int argc, char **argv){
QApplication a(argc,argv);
Ui_MainWindow mainObject;
QMainWindow mainWindow;
mainObject.setupUi(&mainWindow);
mainWindow.show();
return a.exec();
}

The main file includes the constructor of the class ExtendedButton. Its role is to call the parent’s constructor. Another function implemented is mouseReleaseEvent, which is an event handler. You can learn from Qt Assistant, that the method mouseReleaseEvent is an event handler by clicking Qt Widget->QWidget in the right-hand Contents tab, and then click the link reading “events” under detailed description in the pages contents.

The class ExtendedButton is defined in “extendedbutton.h”. Following is the definition:

#include <QtWidgets/QPushButton>

class ExtendedButton:public QPushButton {
public:
ExtendedButton(QWidget *parent=nullptr);
void mouseReleaseEvent(QMouseEvent *event);
};

The main object of the application is defined in “ui_example.h”, the file generated by “Qt Designer”, you better avoid changing it manually if you want to modify the “.ui” file from which it was generated. You’ll see a warning at the beginning. The role of the Class Ui_MainWindow is to contain main window (or central widget) and its underlying widgets as public members. The method setupUi binds them.

### Creating the qmake file

“qmake” is an easy-to-use utility that generates a Makefile to be used by the make command to generate binaries, objects, libraries. etc. Qt Assistant includes a Qt Manual. Following is the content of the example’s qmake file named ‘qmake.pro’:

TARGET=executable
SOURCES+=main.cpp
HEADERS+=extendedbutton.h
FORMS+=example.ui
DESTDIR=bin
QT = core gui
greaterThan(QT_MAJOR_VERSION, 4): QT += widgets

If you want the Make program to create the main header file, you can include the “.ui” file generated by Qt Designer in a variable named “FORMS”. The “make” program in turn will generate a header file from it with the prefix “ui_” added to the “.ui” file name. For example, from a file named “example.ui” the “make” program will generate a header file named “ui_example.h”. In this case, don’t add “ui_example.h” to the variable “HEADERS”.

If you want to know what to add to QT, go to the <Class Category>->C++ Classes and click the Detailed Description link.If you want to run qmake without command line arguments, call the qmake file ‘qmake.pro’.

## Adding Colors to IRC Outgoing Messages

The other day, I participated in a discussion on GimpNet IRC (irc://irc.gimp.org). I saw there a message in which some words were colored. Since my client is Pidgin, I cannot add colors simply by clicking on the Font button, and selecting a color: all the menu options are disabled.

Searching the web for IRC colors, I found that mIRC supports adding colors to the text. If you are not a mIRC user, at least you can find the list of color codes here. The page does not describe how to add colors and other text attributes in other clients, but to learn at least about the sequences to be sent to the server, writing a script is recommended. To find the way to write scripts using the IRC protocol, I recommend using the PERL language. A great place to find PERL modules is the CPAN (Comprehensive PERL Archive Network) site. Search for IRC. A good class to create mIRC color strings is String::IRC – add color codes for mIRC compatible client.

Following is a script I’ve written to print the sequences:

use String::IRC;
use strict;

sub print_char {
my $ch=shift; my$ord=ord($ch); if ($ord<32 or $ord>126){ printf "\033[37;1m<%x>\033[0m",$ord;
} else {
print $ch; } } sub print_string { my$str=shift;
my $len=length($str);
for (my $i=0;$i<$len;$i++){
print_char(substr($str,$i,1));
}
print "\n";
}

my $red=String::IRC->new("Red")->red; print_string "Red:$red";
my $red_underlined=String::IRC->new("Red Underlined")->red->underline; print_string "Red Underlined$red_underlined";
my $red_bold=String::IRC->new("Red Bold")->red->bold; print_string "Red Bold:$red_bold";
my $red_inverse=String::IRC->new("Red Inverse")->red->inverse; print_string "Red Inverse:$red_inverse";

The output of the script is in the following image:

The hex codes of control characters appear in white. They can be added as Unicode characters.

So,

• Unicode character 0x02 begins a bold string or sub-string.
• Unicode character 0x1f begins an underlined string or sub-string.
• Unicode character 0x03 begins a colored string or sub-string when followed by:
• A foreground code
• Foreground and background codes separated by a comma.
• Unicode character 0x0f resumes to the default text format.

### Now, to add a Control Character in Pidgin

First, check that the input method is “System”. To do it, left-click inside the input area and choose the input method:

Use your system’s method to insert a Unicode characterFor example, In Linux/UNIX, type <Ctrl>+<shift>+U followed by the hexadecimal code of the character, and the space or Enter.

## Widgets and Tables in Matplotlib

Matplotlib is a great python library for plotting and graphics. Graphics include formatted text, text paths and tabular data. Mathematical expressions are a good reason to use Matplotlib for rendering text. Matplotlib also supports some widgets one can use for input. If you use Matplotlib widgets, you vetter know how to size and position them unless – for example – you write a program for yourself.

Following is an example of bad code:

from matplotlib import pyplot as plt
from matplotlib.widgets import TextBox
from matplotlib.widgets import Button

fig,ax=plt.subplots()

teextbox=TextBox(ax,"Label:")
button=Button(ax,'Submit')

plt.show()

The code above create to widgets that fill up the same plotting area inside defined Axes object. In the following image, you can see that both the text entered by the user and the button text overlap. In addition. the text entered by the user exceeds the limit of the plotting area.

## Get More Control over Your Widgets

For better results, there are 3 things to do:

• Use separate plotting area for your widgets.
• Set the plotting areas’ positions and sizes.
• Using Event Handlers to control the input length in a TextBox and perform operations.

### Separate Plotting Areas

The command plt.subplots() creates a figure, and a single plotting area, a uni-dimensional array of plotting areas or a bi-dimensional array of plotting areas. According to the number of rows and columns. The default is one row and one column. For example:

fig,ax=plt.subplots(nrows=2)

Returns a column of two plotting areas, To set the number of columns use the keyword argument ncols.

Let us see what happens if we set the number of colums (not adding widgets. yrt) by the following code:

from matplotlib import pyplot as plt
from matplotlib.widgets import TextBox
from matplotlib.widgets import Button

fig,ax=plt.subplots(nrows=2)

plt.show()

The code generates two Axes rectangles as follows:

### Resizing and Positioning a Plotting Area

The Axes rectangle can be resized and positioned using the function matplotlib.axes.Axes.set_position. One of its arguments can be an array whose members are left,bottom,width and height. The position and size is relative to the figure. :

• left=0 means that the Axes begin at the left side of the figure
• left=1 means that the Axes begin at the right side of the figure (which makes them invisible).
• bottom=0 means that the Axes begin at the bottom of the figure
• bottom=1 means that the Axes begin at the top of the figure

The following code resizes the Axes rectangles, and adds the widgets:

from matplotlib import pyplot as plt
from matplotlib.widgets import TextBox
from matplotlib.widgets import Button

fig,ax=plt.subplots(nrows=2)

ax[0].set_position([0.2,0.85,0.7,0.08])
ax[1].set_position([0.495,0.6,0.1,0.1])
teextbox=TextBox(ax[0],"Label:",label_pad=0.01,color='cyan',hovercolor='red')
button=Button(ax[1],'Submit')
plt.show()

ax[0] is the rectangle containing the TextBox

ax[1] is the rectangle containing the box. It’s width is 0.1(10% of that of the figure), and its left edge is position at 0.495, which is 0.5+0.1/2. This makes its horizontal alignment centered.

In the following image you’ll see that the background color of the text box is ‘cyan’, and hovercolor defines the background color when the mouse pointer is over the text box.

### Setting the Input Text’s Maximal Length and Event Handling

Event handling functions can be attached to widgets. Event handling functions can react to button clicks, text changes, submitions by pressing the Enter key, etc.

If you want to restrict the length of the input text in a TextBox, attach an event handling function as follows:

tb.on_text_change(func)

Where func is a function that gets one argument, the text. In this function, you can restrict the number of character. You better set the cursor position as well, because it increases whenever the user types a character, even if the text is changed by the event handler. Following is an example of how to check that the input matches a pattern all the way:

def tc_func(self,inp):
if (len(inp)>self.maxlen):
self.tb.cursor_index=self.curpos
self.tb.set_val(self.val)
return
if (self.decpoint and inp.find('.')<0 and len(inp)>self.maxlen-1):
self.tb.cursor_index=self.curpos
self.tb.set_val(self.val)
return
if (not self.pattern.match(inp)):
self.tb.cursor_index=self.curpos
self.tb.set_val(self.val)
return
self.val=inp
self.curpos=self.tb.cursor_index

From the argument self you can learn that the above function is a member of a class. Wrapping widgets in objects is recommended.

The member ‘cursor_index‘ is the position of the cursor after the event handler finishes its work. set_val sets a new value (or resets it).

The full source from which the code above is taken from my Square Root Calculator found at https://github.com/amity1/SquareRootCalculator

To handle button click events , use the function on_clicked, as follows:

button.on_clicked(click_handler)

The argument passed to the click_handler is an object of type matplotlib.backend_bases.MouseEvent. You can see in the following code how you can learn it:

from matplotlib import pyplot as plt
from matplotlib.widgets import TextBox
from matplotlib.widgets import Button

def click_handler(evt):
print(type(evt))
print("Button clicked with:"+ str(evt.button))

fig,ax=plt.subplots(nrows=2)

ax[0].set_position([0.2,0.85,0.7,0.08])
ax[1].set_position([0.495,0.6,0.1,0.1])
teextbox=TextBox(ax[0],"Label:",label_pad=0.01,color='cyan',hovercolor='red')
button=Button(ax[1],'Submit')
button.on_clicked(click_handler)
plt.show()

The event handler above prints the type of mits argument and the mouse button with which the button widget was clicked. Following is the output:

Button clicked with:MouseButton.LEFT

Button clicked with:MouseButton.MIDDLE

Button clicked with:MouseButton.RIGHT
<class 'matplotlib.backend_bases.MouseEvent'>
Button clicked with:MouseButton.LEFT
<class 'matplotlib.backend_bases.MouseEvent'>
Button clicked with:MouseButton.MIDDLE
<class 'matplotlib.backend_bases.MouseEvent'>
Button clicked with:MouseButton.RIGHT

## Tables

A table is a widget that can be added to an Axes object in addition to other Artists.

There are two ways to create a table:

If you just choose to create a table without specifying loc, the table location in respect to the Axes, chances are you will not be satisfied.

The following code creates such a default table using the factory:

import matplotlib as mpl
from matplotlib import pyplot as plt
from matplotlib.widgets import TextBox
from matplotlib.widgets import Button

fig,ax=plt.subplots()
tab=mpl.table.table(ax,cellColours=[['red','green'],['yellow','blue']])

plt.show()

In the following image generated by the code, you will see that the table is created just under the Axes, and it overlaps the frame x-ticks.

You can create the table somewhere else by setting the loc parameter, you can set a cell’s width and height, set a column width automatically, and align text.

### Setting The Table’s Location and Modify Cells

To set a table location in respect to the Axes, pass the parameter loc with one of the valid codes, for example:

tab=mpl.table.table(ax,cellText=[['Red','Green'],['Yellow','Blue']],loc='upper left'

A default text alignment in a table cell can be defined by passing the parameter cellLoc when creating a new table. When adding a cell, the argument name is loc. The valid values for loc are: ‘left’, ‘center’ and ‘right’

Accessing a table cell is easy as ABC: access the cells as if the table were a bi-dimensional array whose elements are objects of type matplotlib.table.Cell. For example:

tab[row,col]

You can modify text properties using the function set_text_props of the cell object. And you can change its position and size by modifying properties inherited from class matplotlib.patches.Rectangle.

The following code creates a table near the upper left corner of the Axes, sets the column widths to be automatic, changes the color of text cells, and enlarges one of the cells.

import matplotlib as mpl
from matplotlib import pyplot as plt

fig,ax=plt.subplots()
tab=mpl.table.table(ax,cellText=[['Red','Green'],['Yellow','Blue']],
cellColours=[['red','green'],['yellow','blue']],
loc='upper left',cellLoc='left' )
tab.auto_set_column_width(0)
tab.auto_set_column_width(1)
tab[1,1].set_height(0.5)
for i,j in ((0,0),(0,1),(1,1)):
tab[i,j].set_text_props(color='white')

plt.show()

The code above produces the following image:

## Adding a Cell

You can add single cells to a table using the function add_cell of the table.

the function should be called with the row number and column number. The caller has to specify the keyword arguments ‘width’ and ‘height’.

The new cell should be connected to the table, and may influence the heights and widths of celles in the same row or column.

The following code adds a cell in a new column and row:

import matplotlib as mpl
from matplotlib import pyplot as plt

fig,ax=plt.subplots()
tab=mpl.table.table(ax,cellText=[['Red','Green'],['Yellow','Blue']],
cellColours=[['red','green'],['yellow','blue']],
loc='upper left',cellLoc='left')
print ("Table Created")
tab.auto_set_column_width(0)
tab.auto_set_column_width(1)
tab[1,1].set_height(0.5)
for i,j in ((0,0),(0,1),(1,1)):
tab[i,j].set_text_props(color='white')
tab[1,0].set_xy((0,0.8))
tab.AXESPAD=0
cell=tab.add_cell(2,2,height=0.1,width=0.3,text='New Cell',loc='center',facecolor='orange')
plt.show()

In the following image, you can see a new orange cell that has been added to an existing table:

## Creating Windows With Ruby Tk

The Ruby language supports creating windows for GUI (Graphic User Interface). GUI applications are programs that respond to user input, which are usually mouse events, such as clicking buttons, clicking menus, etc.

A GUI application may consist of the following types of objects:

• Widgets – basic GUI objects that can be put directly in the window. Most of them generate events as a response to user actions. A label is a widget, too, but, usually does not generate events.
• Shapes – lines, arcs, circles, polygons and other that belong on a canvas.
• Timers – threads that perform an action the number of times specified and sleep for theĀ  specified duration. From the definition “thread” you can understand that they run in parallel.

The simplest Ruby Tk program is:

require 'tk'
Tk.mainloop

This program displays the following window:

This is the default window. It is displayed on the screen when the line ‘Tk.mainloop’ is performed. Until this window is closed, no commands that are not responses to events will be executed.

“Programing Ruby – The Pragmatic Programmers Guide” suggests that you look at Perl/Tk guides to learn how to use Tk. A good place to look for Perl’s objects and their methods is Active Perl. I’m not going to write here the complete guide to Ruby Tk, but I hope the following chapters will help you understand how it works.

To be continued.