![]() ![]() You can imagine a bounding box as a box that surrounds the object like the image below. One of the simplest forms of collision detection uses what is known as Axis-Aligned Bounding Box (AABB). How can we make a gameObject know when it hits something? That’s the job of the collision detection mechanism. Even worse, it can’t even know whether it hit it or not! Looking good, but our ball isn’t bouncing when hitting the screen edge yet. Vector2 newPosition = (Vector2)transform.position movement Īnd look at our little ball! Going beyond infinity, where no ball set foot before. Vector2 movement = direction * speed * ltaTime So, by solving both equations we can find X and Y! That leaves us with two unknown variables b and c, corresponding to our desired values Y and X, respectively. Θ is our desired angle, which is 45°, and c is the length of our vector, which is 1! What does it have to do with finding our values? Well, take a closer look at the first two equations ( sin and cos). Notice how the vector v ends on the unit circle, having a magnitude of 1.Ī familiar shape arises! That makes a right triangle, which has a lot of useful properties, especially in trigonometry. Let’s name our desired vector as v, and let’s extract its X and Y components as follows: Ok, we know the direction and the magnitude, but we still don’t know what are the values for the X and Y components. But the cool thing is, if we have a vector that starts in the origin and ends inside the circumference of the unit circle, it’ll have a magnitude of 1! This is known as a unit vector. In reality, it’s just a circle that has a radius of 1. That way, it has to have a magnitude of 1.Īre you familiar with the unit circle? If not, take a look at the image below. We already know which direction we want the ball to go (at an angle of 45°), but what about the magnitude? As this vector will only store direction, it shouldn’t interfere with the speed when multiplying both. We’re going to solve this question with the power of (please don’t go away) trigonometry!! The question is, how can we set an angle, like 45°, if we can only specify the X and Y components of a vector? We need a way to get those with only the angle (direction) and the magnitude (length). ![]() When the game starts (and the ball script is enabled), this method will be called and our direction set.įor now, let’s make the ball go to the right and up, diagonally with an angle of 45°, like the image below. Getting a $$ degrees angle is of course possible by computing $arccos(\frac)$.The ball will need an initial direction to starting moving, so where can we set it? The Start method is perfect for this. In the 3D case, your two vectors would be on some plane (the plane that you can get its normal from the cross-product of the two vectors). So there is no real sense in a value in a range larger than $$. The angle from the front will be the opposite of the angle that you see from the back. The dot product will therefore basically measure the length of that vector, but with the correct sign attached to it.īefore reading this answer - Imagine your angle in a 3D space - you can look at it from the "front" and from the "back" (front and back are defined by you). This might be easier to implement in some APIs, and gives a different perspective on what's going on here: The cross product is proportional to the sine of the angle, and will lie perpendicular to the plane, hence be a multiple of $n$. The determinant could also be expressed as the triple product: One condition for this to work is that the normal vector $n$ has unit length. In this case, you can adapt the 2D computation above, including $n$ into the determinant to make its size $3\times3$. Then the axis of rotation will be in direction $n$ as well, and the orientation of $n$ will fix an orientation for that axis. One special case is the case where your vectors are not placed arbitrarily, but lie within a plane with a known normal vector $n$. In this case, the dot product of the normalized vectors is enough to compute angles. One common convention is to let angles be always positive, and to orient the axis in such a way that it fits a positive angle. That axis of rotation does not come with a fixed orientation, which means that you cannot uniquely fix the direction of the angle of rotation either. In 3D, two arbitrarily placed vectors define their own axis of rotation, perpendicular to both. Many programming languages provide a function atan2 for this purpose, e.g.: dot = x1*x2 y1*y2 # dot productĪngle = atan2(det, dot) # atan2(y, x) or atan2(sin, cos) And if you know the cosine and the sine, then you can compute the angle. Just like the dot product is proportional to the cosine of the angle, the determinant is proprortional to its sine. I'm adapting my answer on Stack Overflow.
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