I have a point (node.get World Translation) and four positions of a quad (vertices[4]).
I want to determine if that point is inside the quad or not. and without using shape collision.

â€śI wonder how to translate something from world to local spaceâ€¦ let me check the javadoc just in case this is one of those 1 in 10 times that there is somethingâ€¦â€ť

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/**
* Calculate the area of the specified triangle.
*
* @param triangle (not null, unaffected)
* @return the area (≥0)
*/
public static double area(Triangle triangle) {
Vector3f a = triangle.get1();
Vector3f b = triangle.get2();
Vector3f c = triangle.get3();
Vector3f ab = b.subtract(a);
Vector3f ac = c.subtract(a);
Vector3f cross = ab.cross(ac);
double areaSquared = lengthSquared(cross) / 4.0;
double area = Math.sqrt(areaSquared);
return area;
}
/**
* Calculate the squared length of a vector. Unlike
* {@link com.jme3.math.Vector3f#lengthSquared()}, this method returns a
* double-precision value for precise comparison of lengths.
*
* @param vector input (not null, unaffected)
* @return the squared length (≥0)
*/
public static double lengthSquared(Vector3f vector) {
double xx = vector.x;
double yy = vector.y;
double zz = vector.z;
double result = xx * xx + yy * yy + zz * zz;
return result;
}

I donâ€™t get why you do (x^2)/4 then take the square root of that. You just square then sqrt. The same as just taking abs( cross / 2), which is a property of the cross product. Abs(cross) is equal to the area of the parallelogram formed by the two vectors.