Limiting the Circle with a Rectangle

Questions & Answers
1

Hello everyone.

I want to constrain a circle I created in my project using a rectangle. I watched a few videos and they generally use the same method, but this method does not give the result I want.

I have prepared a visual demo for you below.

I want to constrain the angle I give using the blue circle with the red rectangle. You can see the angle as the green line. The little white circle is the value I got.

205630-ss1.png
205630-ss1.png870×312 6.17 KB

This method works correctly when the angle is 0,90,180,270 etc. However, as you can see below, it does not give the desired result for other values.

205631-ss2.png
205631-ss2.png870×312 6.47 KB

The value I want should be exactly on the green line.

Here’s my code for this demo:

    using UnityEngine;
    
    public class CircleLimiter : MonoBehaviour
    {
        public Vector2 rectangleSize;
        public float circleRadius;
        public float angle;
    
        void OnDrawGizmos()
        {
            Gizmos.color = Color.red;
            Gizmos.DrawWireCube(Vector3.zero, rectangleSize);
    
            Gizmos.color = Color.blue;
            Gizmos.DrawWireSphere(Vector3.zero, circleRadius);
    
            Gizmos.color = Color.green;
            Vector3 positionByAngle = new Vector3(Mathf.Cos(angle * Mathf.Deg2Rad) * circleRadius, Mathf.Sin(angle * Mathf.Deg2Rad) * circleRadius);
            Gizmos.DrawLine(Vector3.zero, positionByAngle);
    
            Gizmos.color = Color.white;
            Gizmos.DrawWireSphere(Limit(positionByAngle, rectangleSize), 0.2f);
        }
    
        Vector2 Limit(Vector2 position, Vector2 limit)
        {
            limit /= limit;
            return new Vector2(
                            Mathf.Clamp(position.x, -limit.x, limit.x),
                            Mathf.Clamp(position.y, -limit.y, limit.y)
            );
        }
    }

I would be very grateful if you could answer my question or direct me to related topics. Thanks in advance.

2

I managed to solve it somehow but I would like to know if there is a better way. After dividing the area into triangles, I got the result I wanted using the right triangle formulas.

Vector3 Limiter(float ang, Vector2 limit)
    {
        Vector3 result = Vector3.zero;
        float x = 0;
        float y = 0;

        float _ang = ang % 360;
        ang = _ang;

        if (_ang < 0)
            ang = 360 + _ang;

        float a = limit.x;
        float b = limit.y;
        float c = Mathf.Sqrt(Mathf.Pow(limit.x, 2) + Mathf.Pow(limit.y, 2));

        float aAngle = Mathf.Acos(a / c) * Mathf.Rad2Deg;
        float bAngle = 90 - aAngle;

        float zoneAngle = 0;

        if (ang >= 0 && ang < aAngle)
        {
            zoneAngle = ang;
            x = a;
            y = a * Mathf.Tan(zoneAngle * Mathf.Deg2Rad);
        }
        else if (ang >= aAngle && ang < aAngle + bAngle * 2)
        {
            zoneAngle = zoneAngleOverride ? zoneAngleOverrideValue : bAngle - (ang - aAngle);
            x = b * Mathf.Tan(zoneAngle * Mathf.Deg2Rad);
            y = b;
        }
        else if (ang >= aAngle + bAngle * 2 && ang < aAngle * 3 + bAngle * 2)
        {
            zoneAngle = zoneAngleOverride ? zoneAngleOverrideValue : aAngle - (ang - bAngle * 2 - aAngle);
            x = -a;
            y = a * Mathf.Tan(zoneAngle * Mathf.Deg2Rad);
        }
        else if (ang >= aAngle * 3 + bAngle * 2 && ang < aAngle * 3 + bAngle * 4)
        {
            zoneAngle = zoneAngleOverride ? zoneAngleOverrideValue : -bAngle + (ang - bAngle * 2 - aAngle * 3);
            x = b * Mathf.Tan(zoneAngle * Mathf.Deg2Rad);
            y = -b;
        }
        else
        {
            zoneAngle = ang;
            x = a;
            y = a * Mathf.Tan(zoneAngle * Mathf.Deg2Rad);
        }

        result = new Vector3(x, y, 0);


        return result;
    }
3

Cool solution! What are you using this for ?