/**
* Calculates the intersection point bnetween the current and two other planes
*
* @param Plane $plane1
* @param Plane $plane2
* @return bool|\Math_Vector3
* @throws InvalidArgumentException
*/
public function calculateIntersectionPointWithTwoPlanes(self $plane1, self $plane2)
{
$n1 = $this->normalVectorNormalized;
$n2 = $plane1->normalVectorNormalized;
$n3 = $plane2->normalVectorNormalized;
$d1 = $this->distanceToOrigin;
$d2 = $plane1->distanceToOrigin;
$d3 = $plane2->distanceToOrigin;
$n2_x_n3 = \Math_VectorOp::crossProduct($n2, $n3);
$n3_x_n1 = \Math_VectorOp::crossProduct($n3, $n1);
$n1_x_n2 = \Math_VectorOp::crossProduct($n1, $n2);
$p = new \Math_Vector3(\Math_VectorOp::add(\Math_VectorOp::add(\Math_VectorOp::scale($d1, $n2_x_n3), \Math_VectorOp::scale($d2, $n3_x_n1)), \Math_VectorOp::scale($d3, $n1_x_n2))->getTuple());
$divisor = \Math_VectorOp::dotProduct($n1, $n2_x_n3);
if ((double) 0 === $divisor) {
throw new \InvalidArgumentException('no point-intersection');
}
$p->scale(1 / $divisor);
return $p;
}
echo date("Y-m-d H:i:s") . "\n";
echo "==\nVector v1: " . $v1->toString() . "\n";
echo "Vector v2: " . $v2->toString() . "\n";
$r = Math_VectorOp::add($v1, $v2);
echo "v1 + v2: " . $r->toString() . "\n";
$r = Math_VectorOp::substract($v1, $v2);
echo "v1 - v2: " . $r->toString() . "\n";
$r = Math_VectorOp::multiply($v1, $v2);
echo "v1 * v2: " . $r->toString() . "\n";
$r = Math_VectorOp::divide($v1, $v2);
echo "v1 / v2: " . $r->toString() . "\n";
echo "==\nVector w1: " . $w1->toString() . "\n";
echo "Vector w2: " . $w2->toString() . "\n";
echo "Vector w3: " . $w3->toString() . "\n";
$r = Math_VectorOp::scale(2.0, $w1);
echo " 2.0 * w1 = " . $r->toString() . "\n";
$r = Math_VectorOp::dotProduct($w1, $w2);
echo "w1 . w2 = {$r}\n";
$r = Math_VectorOp::crossProduct($w2, $w3);
echo "w2 x w3 = " . $r->toString() . "\n";
echo "The triple scalar product of 3 vectors is the volume\r\nof the parallelepiped defined by the vectors. Three coplanar\r\nvectors must give a volume of zero, w1, w2 and w3 are coplanar\n";
$r = Math_VectorOp::tripleScalarProduct($w1, $w2, $w3);
echo "w1 . (w2 x w3) = {$r}\n";
$z = Math_VectorOp::createOne(3);
echo "Now we introduce z : " . $z->toString() . "\n";
echo "and z not being coplanar to w1, w2, or w3:\n";
$r = Math_VectorOp::tripleScalarProduct($z, $w2, $w3);
echo "z * (w2 x w3) = {$r}\n";
$r = Math_VectorOp::angleBetween($z, $w1);
echo "and the angle between z and w1 is {$r} radians\n";
echo "which is " . $r * 180.0 / M_PI . " degrees\n";
/**
* Vector triple scalar product = v1 . (v2 x v3)
*
* @access public
* @param object Math_Vector3 (or subclass) $v1
* @param object Math_Vector3 (or subclass) $v2
* @param object Math_Vector3 (or subclass) $v3
* @return mixed the triple scalar product (float) on success, a PEAR_Error object otherwise
*
* @see isVector3()
* @see dotProduct()
* @see crossProduct()
*/
function tripleScalarProduct($v1, $v2, $v3)
{
if (Math_VectorOp::isVector3($v1) && Math_VectorOp::isVector3($v2) && Math_VectorOp::isVector3($v3)) {
return Math_VectorOp::dotProduct($v1, Math_VectorOp::crossProduct($v2, $v3));
} else {
return PEAR_Error("All three vectors must be of the same type");
}
}
/**
* Vector triple scalar product = v1 . (v2 x v3)
*
* @param object Math_Vector3 (or subclass) $v1
* @param object Math_Vector3 (or subclass) $v2
* @param object Math_Vector3 (or subclass) $v3
* @return mixed the triple scalar product (float) on success
* @throws InvalidArgumentException
*
* @see isVector3()
* @see dotProduct()
* @see crossProduct()
*/
public static function tripleScalarProduct($v1, $v2, $v3)
{
if (Math_VectorOp::isVector3($v1) && Math_VectorOp::isVector3($v2) && Math_VectorOp::isVector3($v3)) {
return Math_VectorOp::dotProduct($v1, Math_VectorOp::crossProduct($v2, $v3));
}
throw new InvalidArgumentException("All three vectors must be of the same type");
}
