public final class vector { // Class to manipulate a 3D vector
        private double x, y, z;
        public vector() { // Empty vector
                x = 0;
                y = 0;
                z = 0;
        }
        public vector(double x, double y, double z) { // Create a vector
                this.x = x;
                this.y = y;
                this.z = z;
        }
        public vector(vector v) { // Create a copy of a vector
                x = v.x;
                y = v.y;
                z = v.z;
        }
        public vector(vector v1, vector v2) { // Create a vector by vector product
                mult(v1, v2);
                norm();
        }
        public double mult(vector v) { // Scalar product
                return x * v.x + y * v.y + z * v.z;
        }
        private double norm2() { // Square of length
                return x * x + y * y + z * z;
        }
        public double cosAng(vector v) { // Cosine of angle between vectors
                return mult(v) / Math.sqrt(norm2() * v.norm2());
        }
        private void norm() { // Normalize vector
                double d = Math.sqrt(norm2());
                x /= d;
                y /= d;
                z /= d;
        }
        public void add(vector v) { // Add vector
                x += v.x;
                y += v.y;
                z += v.z;
        }
        public void addmult(vector v, double d) { // Add scaled vector
                x += v.x * d;
                y += v.y * d;
                z += v.z * d;
        }
        public void addmultnorm(vector v, double d) { // With normalization
                addmult(v, d);
                norm();
        }
        public void sub(vector v) { // Subtract vector
                x -= v.x;
                y -= v.y;
                z -= v.z;
        }
        public void copy(vector v) { // Copy a vector
                x = v.x;
                y = v.y;
                z = v.z;
        }
        private void mult(vector v1, vector v2) { // Vector product
                x = v1.y * v2.z - v1.z * v2.y;
                y = v1.z * v2.x - v1.x * v2.z;
                z = v1.x * v2.y - v1.y * v2.x;
        }
        public void multnorm(vector v1, vector v2) { // With normalization
                mult(v1, v2);
                norm();
        }
        public void rotateX(double cos, double sin) { // Rotation about X axis
                double y = this.y * cos + z * sin;
                z = z * cos - this.y * sin;
                this.y = y;
        }
        public void rotateY(double cos, double sin) { // Rotation about Y axis
                double x = this.x * cos + z * sin;
                z = z * cos - this.x * sin;
                this.x = x;
        }
        public void rotateZ(double cos, double sin) { // Rotation about Z axis
                double x = this.x * cos + y * sin;
                y = y * cos - this.x * sin;
                this.x = x;
        }
        private static String parameter(String param, char suffix, double d) {
                if (d <= -1 || d >= 1 || d == 0) return "<param name=\"" + param + suffix + "\" value=\"" + d + "\">";
                else if (d < 0) return "<param name=\"" + param + suffix + "\" value=\"-" + String.valueOf(10 - d).substring(1) + "\">";
                else return "<param name=\"" + param + suffix + "\" value=\"" + String.valueOf(10 + d).substring(1) + "\">";
        }
        public void writeParameters(String param) {
                System.err.println(parameter(param, 'x', x));
                System.err.println(parameter(param, 'y', y));
                System.err.println(parameter(param, 'z', z));
        }
}