基于三个2D向量的三角形区域反转实现咨询（游戏开发）

Got it, let's tackle this problem—marking everything outside a triangle defined by three 2D vectors for your game dev workflow. Here's a straightforward, practical approach that’s optimized for game performance and ease of integration:

The key here is to first figure out how to tell if a point is inside the triangle, then simply invert that logic to mark points outside. The most efficient method for 2D games (especially for real-time checks) uses cross products—no fancy math libraries required.

Here's the breakdown:
For a triangle with vertices A, B, C, and a test point P:

1. Calculate three cross products:
   • Cross(B - A, P - A) (checks which side of edge AB the point P is on)
   • Cross(C - B, P - B) (checks which side of edge BC the point P is on)
   • Cross(A - C, P - C) (checks which side of edge CA the point P is on)
2. If all three cross products have the same sign (all positive, all negative, or zero), the point is inside (or on the edge of) the triangle.
3. To mark the outside area, we just check if this condition is not true.

Let's turn this into code that works with most game engines. I'll use a simple C# struct for 2D vectors (adjust this to match your engine's built-in vector type, like Unity's Vector2 or Unreal's FVector2D):

// Basic 2D vector helper (replace with your engine's vector if needed)
public struct Vec2
{
    public float X;
    public float Y;

    public Vec2(float x, float y) { X = x; Y = y; }

    // Subtraction operator for vector differences
    public static Vec2 operator -(Vec2 a, Vec2 b) => new Vec2(a.X - b.X, a.Y - b.Y);

    // 2D cross product (returns scalar z-component of the 3D cross product)
    public static float Cross(Vec2 a, Vec2 b) => a.X * b.Y - a.Y * b.X;
}

// Checks if a point is inside or on the edge of the triangle
bool IsPointInsideTriangle(Vec2 testPoint, Vec2 triA, Vec2 triB, Vec2 triC)
{
    // Calculate cross products for each edge
    float crossAB = Vec2.Cross(triB - triA, testPoint - triA);
    float crossBC = Vec2.Cross(triC - triB, testPoint - triB);
    float crossCA = Vec2.Cross(triA - triC, testPoint - triC);

    // Check if all cross products are non-negative OR all are non-positive
    bool allNonNegative = (crossAB >= 0) && (crossBC >= 0) && (crossCA >= 0);
    bool allNonPositive = (crossAB <= 0) && (crossBC <= 0) && (crossCA <= 0);

    return allNonNegative || allNonPositive;
}

// Reverse the logic to mark points outside the triangle
bool ShouldMarkAsOutsideArea(Vec2 testPoint, Vec2 triA, Vec2 triB, Vec2 triC)
{
    // Just invert the inside check result
    return !IsPointInsideTriangle(testPoint, triA, triB, triC);
}

Since game dev often involves checking lots of points (like grid cells, pixels, or colliders), here are some ways to speed things up:

• Bounding Box Pre-Check: First calculate the triangle's axis-aligned bounding box (AABB). If a point is outside this box, you can immediately mark it as outside the triangle without running the cross product checks. This cuts down on unnecessary computations.
• Use Engine Built-Ins: Most game engines have a built-in point-in-triangle function (e.g., Unity's Geometry.TestPointInTriangle). Just call that and invert the result—no need to reinvent the wheel.
• Render-Time Masking: If you're trying to draw a visual mask of the outside area, use your engine's stencil buffer:
  1. Draw the entire screen with your "outside" color.
  2. Enable stencil testing, then draw the triangle to set the stencil buffer for its area.
  3. Clear the stencil area, leaving only the outside color visible.

内容的提问来源于stack exchange，提问作者Mobilpadde