Exterior bisecting angle and tangent

demo.java

void testBisector() {
	PVector C = new PVector(100, 300);
	PVector B = new PVector(mouseX, mouseY);
	PVector A = new PVector(500, 500);
	float r = 100;

	float[] angle = new float[1]; // To store the calculated angle
	PVector point = findPointOnBisector(A, B, C, r, angle);

	stroke(0);
	strokeWeight(2);
	text(degrees(angle[0]), 10, 10);

	// Draw vectors
	line(A.x, A.y, B.x, B.y);
	line(B.x, B.y, C.x, C.y);

	// Draw points
	fill(255, 0, 0);
	ellipse(A.x, A.y, 10, 10);
	ellipse(B.x, B.y, 10, 10);
	ellipse(C.x, C.y, 10, 10);

	// Draw result point
	fill(0, 255, 0);
	ellipse(point.x, point.y, 10, 10);

	// Draw line from B to result point
	stroke(0, 255, 0);
	line(B.x, B.y, point.x, point.y);

	// Draw perpendicular vector
	PVector tangent = new PVector(-sin(angle[0]), cos(angle[0]));
	tangent.mult(50); // Scale vector for visibility
	PVector endTangent = PVector.add(point, tangent);
	stroke(255, 0, 0);
	line(point.x, point.y, endTangent.x, endTangent.y);
	fill(0);
	text("Perpendicular Vector", endTangent.x, endTangent.y);
}

PVector findPointOnBisector(PVector A, PVector B, PVector C, float r, float[] angle) {
	// Calculate vectors
	PVector v1 = PVector.sub(B, A);
	PVector v2 = PVector.sub(C, B);

	// Normalize vectors
	PVector u1 = v1.copy().normalize();
	PVector u2 = v2.copy().normalize();

	// Add normalized vectors (negating u1 for exterior angle)
	PVector w = PVector.sub(u2, u1);

	// Normalize the result
	w.normalize();

	w.mult(r);
	PVector result = PVector.sub(B, w);

	if (angle != null) {
		// Calculate the angle of the line tangent to the line from B to result point
		PVector tangentVector = PVector.sub(result, B);
		angle[0] = atan2(tangentVector.y, tangentVector.x) - PI; // Subtract HALF_PI to rotate 90 degrees CCW
		angle[0] = (angle[0] + TWO_PI) % TWO_PI; // Normalize angle to be between 0 and TWO_PI
	}

	return result;
}