This application is the result of joint efforts by Petar Samardžić and Momčilo Mrkaić as part of a project for our Object-Oriented Programming class. Since this was a project for our high-school class, some of the words/names in the code are in Serbian.

• Attributes

The only attribute is float [,] mat, which represents the given matrix.

• Constructors

Empty constructor and a constructor based on attributes.

• Properties

Properties N and M, which return the length and width of the matrix, and the Mat property, which can set and return the matrix.

• Operators

The * operator for matrix multiplication.

This class inherits from the Matrica class.

• Attributes

We have a static attribute NT that indicates the current number of created points, string name, and Color color attributes.

• Constructors

Copy constructor, empty constructor, and a constructor based on attributes.

• Properties

Properties to return the name, color, x, and y coordinates of the point, and a PointF property that returns a PointF type point.

• Methods

void Crtaj(graphics, scaling factor, origin) - for drawing the point. float Rastojanje(Tacka T) - distance from another point. float Rastojanje(Prava p) - distance from a line. float Rastojanje(Duz d) - distance from a segment. float Rastojanje(Krug k) - distance from the center of a circle.

We have created methods like Najblizi that return the closest object to the given point (the index of that object in the corresponding array). We did this so that we can highlight an object if someone clicks in its vicinity, allowing the user to select the object closest to where they clicked, rather than having to click exactly on the pixel where the object is located.

int Najblizi(array of lines containing all created lines) - the closest line to the given point. int Najblizi(array of segments) - the closest segment to the given point. int Najblizi(array of circles) - the closest circle to the given point. int Najblizi(array of points) - the closest point to the given point.

Now we have a series of classes that inherit from the Matrica class. They represent matrices of isometric transformations. When, for example, we want to translate a point, we obtain its image by multiplying the matrix of that point by the translation matrix. This is why we represent points and isometries in the form of matrices. In the following four classes, we have only one constructor that creates the matrix for that isometry. The classes are: Translacija, Rotacija, Homotetija, and Refleksija.

• Attributes

We have a static attribute NP that indicates the number of created lines, float k, float n attributes (we represent a line as y = k*x + n), and a string name.

• Constructors

Constructor with two points and a name, and a constructor based on attributes.

• Properties

Properties to return the coefficient, intersection with the y-axis, and name.

• Methods

void Crtaj(graphics, scaling factor, origin, array of objects, object type, RadioButton showhide, pictureBox) - method for drawing the line. bool Pripada(Tacka T) - whether the point belongs to the line.

Prava Normala(Tacka T) - the normal from a point to the line. Prava Paralela(Tacka T) - a line parallel to the given line through a point.

double Ugao(Prava p) and double Ugao(Duz d) - the angle between the given line and another line, or segment.

Prava SimetralaUgla(Prava p) - the angle bisector between the given line and another line. Prava SimetralaUgla(Duz d) - the angle bisector between the given line and a segment.

Then we have Presek methods that return a Tacka type object, i.e., the intersection point of the given line with a segment, another line, or a circle.

The last methods are transformations of the given line using isometric transformations.

A segment is quite similar to a line, so we made it inherit from the Line class.

• Attributes

We have a static attribute ND that indicates the number of created segments, and attributes Point A and Point B, which are the endpoints of the segment.

• Constructors

Constructor based on attributes.

• Properties

Properties FirstPoint and SecondPoint, which return the first and second points of the segment.

• Methods

New methods that are not present in the Prava class are: Prava Simetrala() - the bisector of the given segment.

void PravilanMnogougao(number of vertices, array of points, array of segments, array of objects) - create a regular polygon with n sides, where one side is the given segment. Also, add the newly obtained points and segments to the corresponding arrays.

• Attributes

We have a static attribute NK that indicates the number of created circles. Point C is the center of the circle, double r is the radius, and we also have a string name.

• Constructors

Constructors based on attributes, constructors with 3 points (needed for the construction of a circle), constructors with 2 points (center and a point on the circle), and constructors with a segment and a point (compass).

• Properties

Properties to return the center, radius, and name.

• Methods

We have methods for drawing the circle, checking if a point belongs to the circle, finding intersections of the circle with other objects, and isometric transformations.

What's new for the circle are tangents from a point to the circle and inversion.

void Tangente(Tacka T, array of lines, array of objects) - if the point belongs to the circle, it returns one tangent; if not, it creates both tangents, if the point is inside the circle, it does nothing.

In inversions, we have 5 functions: Tacka Inverzija(Tacka T) - the inverse image of a point relative to the circle, which is the second point; Prava Inverzija(Prava p) - the inverse image of a line relative to the circle when the center of the circle belongs to the line, which returns a line; Krug Inverzija(Prava p) - the inverse image of a line relative to the circle when the line does not contain the center of the circle, which returns a circle; Krug Inverzija(Krug k) - the inverse image of a circle when the circle does not contain the center of inversion, which is a new circle; Prava Inverzija(Krug k) - the inverse image of a circle when it contains the center of inversion, which results in a new line.

• Initialization

Setting static attributes (origin, system size - constant k). Initialize arrays of objects (all together), points, lines, segments, and circles. When adding each object for use, place it in the appropriate array and register changes by increasing the number of objects in each array.

• Variables

Introduce all the variables that will be needed and define the arrays mentioned earlier.

• Methods

Formulate the calls to all methods from the classes related to drawing: Reset, resets the drawing state - finishing the construction of an object, sets the values of variables j1, j2, j3 to 0, and returns the initial color of the points; Undo, go back one step (each step is registered); Labeling, assign names to the introduced objects; Closest, for a given point, find the object from the array of objects that is closest to it, where the distance between objects is defined in the classes; Add, add objects to the appropriate arrays.

• Paint

Color the points introduced by clicking on the surface in blue, and the points obtained as intersections

of objects (e.g., the intersection of two lines) in black. In the drawing state, when we select a point for use, it becomes green.

• Radio Buttons

Introduce the necessary objects of the RadioButton class to select the option we want when drawing (by selecting the corresponding Radio Button, we execute the desired action).

• Zoom

Increase (zoom in) or decrease (zoom out) the scaling factor k, which results in changing the sizes of the shapes we've drawn.

• Obrisi sve

Clear the entire content, clean the drawing surface.

• Pomeraj

By clicking the button, call the Undo method.

• Move

Translate the drawing surface by selecting two points, and translate the selected object by the vector determined by those points.

• Mouse Click

• Tacka

By clicking on the surface, create a new point, add it to the arrays of objects and points, and color it blue.

• Duz

By clicking on two points and choosing the Crtanje Duzi option, create a new segment, add it to the arrays of objects and segments.

• Prava

By clicking on two points and choosing the Crtanje Prave option, create a new line, add it to the arrays of objects and lines.

• Paralela / Normala

By clicking on a point and a line, construct a parallel or normal line through that point, then add it to the arrays of lines and objects.

• Simetrala ugla

Select two lines and an angle vertex, construct the angle bisector, add it to the arrays of lines and objects.

• Simetrala duzi

Select two points and use this option to construct the segment bisector between those two points, then add it to the arrays of lines and objects.

• Mnogougao

Select a segment and use this option to specify the number of vertices for the polygon. Each subsequent vertex is constructed by rotating the previous one around the last one for an angle of (n-2) * pi/n, resulting in a regular n-gon.

• Tangente

By selecting a point and a circle, use this option to construct two tangents from this point to the given circle if it is not located inside the circle. These two lines are added to the arrays of lines and objects.

• Presek

By selecting two objects (lines/segments/circles), construct points that are the intersections of those objects.

• Duz date duzine

By selecting a point and entering the desired length, construct a segment of that length, parallel to the x-axis of the coordinate system.

• Ugao date velicine

By selecting the angle vertex, an arm, and entering the angle size, construct the second arm of the angle.

• Merenje duzi/ugla

By selecting one of these options, calculate and display its size.

• Centar i tacka na krugu

Select the center of the circle and a point on it to construct the desired circle.

• Centar i poluprecnik

Select the center and enter the radius to construct the circle.

• Tri tacke

Select three points to construct a circle through them using this option.

• Nalazenje centra kruga

By selecting a specific circle, construct a point that is its center.

• Homotetija

By selecting the center of the homothety and entering the coefficient, construct the object obtained by the given homothety and place it in the appropriate arrays.

• Translacija

By selecting two points, translate the selected object by the vector determined by those points.

• Refleksija

By selecting the axis of reflection and the object, use this option to map the selected object over that line.

• Rotacija

By selecting the center of rotation, clicking on the point to be rotated, and entering the rotation angle (in degrees), construct the rotated point.

• Inverzija

By selecting a point and a circle, use this option to construct the inverse image of the point relative to the given circle (analyzing whether it is inside the circle, outside it, or on the circle).