Finding points on a rectangle at a given angle

Question

I\'m trying to draw a gradient in a rectangle object, with a given angle (Theta), where the ends of the gradient are touching the perimeter of the rectangle.

Answer 1

Unreal Engine 4 (UE4) C++ Version.

Note: This is based off of Olie's Code. Based on Belisarius's Answer. Give those guys upvotes if this helps you.

Changes: Uses UE4 syntax and functions, and Angle is negated.

Header

UFUNCTION(BlueprintCallable, meta = (DisplayName = "Project To Rectangle Edge (Radians)"), Category = "Math|Geometry")
static void ProjectToRectangleEdgeRadians(FVector2D Extents, float Angle, FVector2D & EdgeLocation);

Code

void UFunctionLibrary::ProjectToRectangleEdgeRadians(FVector2D Extents, float Angle, FVector2D & EdgeLocation)
{
    // Move theta to range -M_PI .. M_PI. Also negate the angle to work as expected.
    float theta = FMath::UnwindRadians(-Angle);

    // Ref: http://stackoverflow.com/questions/4061576/finding-points-on-a-rectangle-at-a-given-angle
    float a = Extents.X; // "a" in the diagram | Width
    float b = Extents.Y; // "b"                | Height

    // Find our region (diagram)
    float rectAtan = FMath::Atan2(b, a);
    float tanTheta = FMath::Tan(theta);

    int region;
    if ((theta > -rectAtan) && (theta <= rectAtan))
    {
        region = 1;
    }
    else if ((theta > rectAtan) && (theta <= (PI - rectAtan)))
    {
        region = 2;
    }
    else if ((theta > (PI - rectAtan)) || (theta <= -(PI - rectAtan)))
    {
        region = 3;
    }
    else
    {
        region = 4;
    }

    float xFactor = 1.f;
    float yFactor = 1.f;

    switch (region)
    {
        case 1: yFactor = -1; break;
        case 2: yFactor = -1; break;
        case 3: xFactor = -1; break;
        case 4: xFactor = -1; break;
    }

    EdgeLocation = FVector2D(0.f, 0.f); // This rese is nessesary, UE might re-use otherwise. 

    if (region == 1 || region == 3)
    {
        EdgeLocation.X += xFactor * (a / 2.f);              // "Z0"
        EdgeLocation.Y += yFactor * (a / 2.f) * tanTheta;
    }
    else // region 2 or 4
    {
        EdgeLocation.X += xFactor * (b / (2.f * tanTheta)); // "Z1"
        EdgeLocation.Y += yFactor * (b / 2.f);
    }
}