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====================

User prompt 1 of 2 - 26/08/2025, 6:09:24 pm:
Math used for UI rotation of the image is based around simple Trigonometry.
In the first part when the mouse is pressed we get the distance from mouse to image corner (cyan line image 1) 
In second part we get desired angle from mouse horizontal location (image 2)
In third part we use the angle to calculate the new position of the image corner (image 1)
In forth part when mouse is released we reset image position


=== First step when mouse pressed
We need to calculate the distance from mouse and image corner.
$$
\begin{align}  
mouseStart &= mouseV\\
sizeOfVectorMI &= \sqrt{(mouseV_x - imageV_x)² + (mouseV_y - imageV_y)²}\\
oldAngleOfVectorMI &= atan2(imageV_x - mouseV_x, imageV_y - mouseV_y)\\
\end{align}  
$$
sizeOfVectorMI is the (cyan line image1)  
And we need to remember the starting position (green point / orange line image 1)


=== Second step while mouse is pressed
First we need to calculate rotation of the image based on horizontal distance of the mouse position from the start point.
We get this by 
$$
\begin{align}  
dist &= mouseV_x - mouseStart_x \\
l &= \frac{dist}{screenWidth}\\
rotation &= lerp(45,-45, \frac{l + 1}{2})\\
newAngleOfVectorMI &= (\frac{rotation * \pi}{180}) + oldAngleOfVectorMI\\
\end{align}
$$
Can now get vector from the mouse to the corner of the image

$$
\begin{align}  
vectorMI_x &= sizeOfVecorMI * cos(newAngleOfVectorMI)\\
vectorMI_y &= sizeOfVecorMI * sin(newAngleOfVectorMI)\\
\end{align}
$$
From the vector we can get corner of the image and rotation of the image
$$
\begin{align}  
imageV_x &= vectorMI_x + mouseV_x\\
imageV_y &= vectorMI_y + mouseV_y\\
imageRotation &= 90 + rotation\\
\end{align}
$$

With position of the corner we can draw the image from the corner with angle imageRotation

=== Third step when mouse is released 
We reset values
$$
\begin{align}
imageRotation &= 90 \\
imageV &= orgImageV\\
\end{align}
$$


REFERENCE

https://en.wikipedia.org/wiki/Atan2#Definition_and_computation
$$

angle = atan2(y, x) = 
\begin{cases} 
\arctan(\frac{y}{x}) & \text{if } x > 0 \\
\arctan(\frac{y}{x}) + \pi & \text{if } y \geq 0 \text{ and } x < 0 \\
\arctan(\frac{y}{x}) - \pi & \text{if } y < 0 \text{ and } x < 0 \\
\frac{\pi}{2} & \text{if } x = 0 \text{ and } y > 0 \\
-\frac{\pi}{2} & \text{if } x = 0 \text{ and } y < 0 \\
\text{undefined} & \text{if } x = 0 \text{ and } y = 0
\end{cases}

$$


![[cordinats_show_mouse_picture.jpg|200]]

![[show_mouse_movement.jpg |200]]


```cpp
float Vector2Distance(Vector2 v1, Vector2 v2)
{
    float result = sqrtf((v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y));
    return result;
}
```


```cpp
Vector2 mouseV = GetMousePosition();
if (IsMouseButtonPressed(MOUSE_BUTTON_LEFT))
{
	mouseStart = mouseV;
	sizeOfVectorMI = Vector2Distance(mouseStart, newPosition);
	oldAngleOfVectorMI = std::atan2(newPosition.x - mouseStart.x, newPosition.y - mouseStart.y);
}

if (IsMouseButtonDown(MOUSE_BUTTON_LEFT))
{
	
	float dist = mouseV.x - mouseStart.x;
	float l = dist / screenWidth;
	rotation = Lerp(45.0f, -45.0f, (l + 1) / 2);
	float newAngleOfVectorMI = ((rotation*PI) / 180.0f) + oldAngleOfVectorMI;
	
	Vector2 vectorMI = {
		.x = sizeOfVectorMI * std::sin(newAngleOfVectorMI), 
		.y = sizeOfVectorMI * std::cos(newAngleOfVectorMI)
	};
	
    imageV.x = vectorMI.x + mouseV.x;
    imageV.y = vectorMI.y + mouseV.y;
}

if (IsMouseButtonReleased(MOUSE_BUTTON_LEFT))
{
    rotation = 0.0f;
    newPosition = orgPosition;
}
```
can you format and rewrite to unify it.

directy output the finished text dont respond with enything else

GPT-4o mini:
== UI Image Rotation Using Trigonometry

The process of rotating an image based on mouse movement involves several steps, utilizing basic trigonometric principles. Below is a unified and formatted explanation of the steps involved.

=== Step 1: Mouse Pressed

When the mouse is pressed, we calculate the distance from the mouse to the image corner.

$$
\begin{align}  
mouseStart &= mouseV\\
sizeOfVectorMI &= \sqrt{(mouseV_x - imageV_x)² + (mouseV_y - imageV_y)²}\\
oldAngleOfVectorMI &= \text{atan2}(imageV_x - mouseV_x, imageV_y - mouseV_y)\\
\end{align}  
$$

- *sizeOfVectorMI* represents the distance (cyan line in image 1).
- We also store the starting position (green point/orange line in image 1).

=== Step 2: While Mouse is Pressed

Next, we calculate the rotation of the image based on the horizontal distance of the mouse position from the starting point.

$$
\begin{align}  
dist &= mouseV_x - mouseStart_x \\
l &= \frac{dist}{screenWidth}\\
rotation &= \text{lerp}(45, -45, \frac{l + 1}{2})\\
newAngleOfVectorMI &= \left(\frac{rotation \cdot \pi}{180}\right) + oldAngleOfVectorMI\\
\end{align}
$$

Now, we can derive the vector from the mouse to the corner of the image:

$$
\begin{align}  
vectorMI_x &= sizeOfVectorMI \cdot \cos(newAngleOfVectorMI)\\
vectorMI_y &= sizeOfVectorMI \cdot \sin(newAngleOfVectorMI)\\
\end{align}
$$

Using this vector, we can determine the new position of the image corner and its rotation:

$$
\begin{align}  
imageV_x &= vectorMI_x + mouseV_x\\
imageV_y &= vectorMI_y + mouseV_y\\
imageRotation &= 90 + rotation\\
\end{align}
$$

With the position of the corner established, we can draw the image from this corner at the angle *imageRotation*.

=== Step 3: Mouse Released

Upon releasing the mouse, we reset the values:

$$
\begin{align}
imageRotation &= 90 \\
imageV &= orgImageV\\
\end{align}
$$

=== Reference for atan2 Function

The *atan2* function is defined as follows:

$$
\text{angle} = \text{atan2}(y, x) = 
\begin{cases} 
\arctan\left(\frac{y}{x}\right) & \text{if } x > 0 \\
\arctan\left(\frac{y}{x}\right) + \pi & \text{if } y \geq 0 \text{ and } x < 0 \\
\arctan\left(\frac{y}{x}\right) - \pi & \text{if } y < 0 \text{ and } x < 0 \\
\frac{\pi}{2} & \text{if } x = 0 \text{ and } y > 0 \\
-\frac{\pi}{2} & \text{if } x = 0 \text{ and } y < 0 \\
\text{undefined} & \text{if } x = 0 \text{ and } y = 0
\end{cases}
$$

=== C++ Implementation

```cpp
float Vector2Distance(Vector2 v1, Vector2 v2)
{
    float result = sqrtf((v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y));
    return result;
}

Vector2 mouseV = GetMousePosition();
if (IsMouseButtonPressed(MOUSE_BUTTON_LEFT))
{
    mouseStart = mouseV;
    sizeOfVectorMI = Vector2Distance(mouseStart, newPosition);
    oldAngleOfVectorMI = std::atan2(newPosition.x - mouseStart.x, newPosition.y - mouseStart.y);
}

if (IsMouseButtonDown(MOUSE_BUTTON_LEFT))
{
    float dist = mouseV.x - mouseStart.x;
    float l = dist / screenWidth;
    rotation = Lerp(45.0f, -45.0f, (l + 1) / 2);
    float newAngleOfVectorMI = ((rotation * PI) / 180.0f) + oldAngleOfVectorMI;
    
    Vector2 vectorMI = {
        .x = sizeOfVectorMI * std::sin(newAngleOfVectorMI), 
        .

--------------------

User prompt 2 of 2 - 26/08/2025, 6:17:49 pm:
continue

GPT-4o mini:
```cpp
        .y = sizeOfVectorMI * std::cos(newAngleOfVectorMI)
    };
    
    imageV.x = vectorMI.x + mouseV.x;
    imageV.y = vectorMI.y + mouseV.y;
}

if (IsMouseButtonReleased(MOUSE_BUTTON_LEFT))
{
    rotation = 0.0f;
    newPosition = orgPosition;
}
```

This C++ code snippet implements the logic for rotating an image based on mouse movements. It calculates the distance and angle between the mouse position and the image corner, updates the image's position and rotation while the mouse is pressed, and resets the values when the mouse is released. 

By following these steps, you can achieve a smooth and intuitive image rotation effect in your UI.