如何修改角度ang以生成沿直线P1P2反射的圆弧？

To create an arc reflected across the line defined by points P1 and P2, you have two straightforward approaches—either reflect each generated point directly, or adjust your angle calculations and use a reflected center. Here's how to implement both:

Approach 1: Reflect Each Arc Point (Simplest Implementation) #

This method takes your original arc points and mirrors them across the line P1P2. It's easy to drop into your existing code without major changes.

First, add a helper function to calculate the reflection of a point over a line:

Vector2 ReflectPoint(Vector2 point, Vector2 p1, Vector2 p2)
{
    float dx = p2.x - p1.x;
    float dy = p2.y - p1.y;
    float lenSq = dx * dx + dy * dy;
    
    // Guard against division by zero if P1 and P2 are identical
    if (lenSq < 0.0001f)
        return point;
    
    // Calculate projection of the point onto the line P1-P2
    float t = ((point.x - p1.x) * dx + (point.y - p1.y) * dy) / lenSq;
    float projX = p1.x + t * dx;
    float projY = p1.y + t * dy;
    
    // Compute the reflected point (twice the projection minus the original point)
    return new Vector2(2 * projX - point.x, 2 * projY - point.y);
}

Then modify your existing loop to reflect each generated point:

// Assume P1 and P2 are your line endpoints, defined elsewhere
for (int i = 0; i <= pts; i++) { 
    // Generate original arc point
    float x = center.x + radius * Mathf.Cos(ang * Mathf.Deg2Rad); 
    float y = center.y + radius * Mathf.Sin(ang * Mathf.Deg2Rad); 
    Vector2 originalPoint = new Vector2(x, y);
    
    // Reflect the point over line P1-P2
    Vector2 reflectedPoint = ReflectPoint(originalPoint, P1, P2);
    
    // Update the Line Renderer
    arcLine.positionCount = i + 1; 
    arcLine.SetPosition(i, reflectedPoint); 
    
    // Increment angle as before
    ang += (float)totalAngle / pts; 
}

Approach 2: Generate Reflected Arc Directly #

If you prefer to generate the reflected arc without first creating the original points, you can adjust your angle calculations and use the reflected center of the original arc. This works because reflection preserves the arc's radius and total angle span (totalAngle remains unchanged).

First, compute the reflected center and the angle of line P1P2:

Vector2 reflectedCenter = ReflectPoint(center, P1, P2); // Use the same helper function as above
Vector2 lineDir = P2 - P1;
float lineAngleDeg = Mathf.Atan2(lineDir.y, lineDir.x) * Mathf.Rad2Deg; // Convert to degrees

Then generate the arc using the reflected center and adjusted angles:

float initialAng = ang; // Store the starting angle to avoid modifying the original variable
for (int i = 0; i <= pts; i++) { 
    // Calculate the original angle for this segment
    float currentAng = initialAng + i * (float)totalAngle / pts;
    
    // Reflect the angle over the line's angle: reflected_angle = 2 * line_angle - original_angle
    float reflectedAng = 2 * lineAngleDeg - currentAng;
    
    // Generate the reflected arc point
    float x = reflectedCenter.x + radius * Mathf.Cos(reflectedAng * Mathf.Deg2Rad); 
    float y = reflectedCenter.y + radius * Mathf.Sin(reflectedAng * Mathf.Deg2Rad); 
    
    // Update the Line Renderer
    arcLine.positionCount = i + 1; 
    arcLine.SetPosition(i, new Vector2(x, y)); 
}

Key Notes: #

• totalAngle stays the same because reflection doesn't change the arc's angular span (e.g., a 90-degree arc remains 90 degrees after reflection).
• Both methods will produce identical results—choose the one that fits your code structure best.
• The helper function handles edge cases like P1 and P2 being the same point (returns the original point instead of crashing).

内容的提问来源于stack exchange，提问作者Hilarious404