Collisions can be determined by testing for line intersections. Imagine a line representing the ground and an object above, falling down. At time t1, take the center point p1 of the object. At time t2, move the object down and take the center point p2 of the object.
If the line formed by endpoints (p1, p2) intersect the ground line, a collision has occurred. On a collision, reset the object to its original position before the movement.
When a collision occurs, be sure to reset the object by the same point used to determine the line intersection. In this example, I use the center point, so the object should be reset by the center point, not its actual x, y (usually top left) coordinate. It is not always the case that resetting by the x, y coordinate is sufficient. This can be seen in the following picture.
If the line formed by endpoints (p1, p2) intersect the ground line, a collision has occurred. On a collision, reset the object to its original position before the movement.
When a collision occurs, be sure to reset the object by the same point used to determine the line intersection. In this example, I use the center point, so the object should be reset by the center point, not its actual x, y (usually top left) coordinate. It is not always the case that resetting by the x, y coordinate is sufficient. This can be seen in the following picture.
It can be seen that even if the object isn't moving, but its size changes, a line intersection can occur, and resetting the object to its x, y position will leave the object's center point below the ground. This results in falling through the floor. Subsequent move operations will not detect a line intersection, and the object will continue to fall.
Resetting by the object's center point (the same point used to detect the line intersection) results in correct collision handling.
This can be extended to sloped lines. Move on x and test for a line intersection. If an intersection occurs, reset the object's position and determine the arctangent theta of the line. Move the object on x by the cosine of theta, and move on y by the sine of theta. Test again for a line intersection. If an intersection occurs, reset the object and stop.
Think about why this works. On flat ground, the entirety of our horizontal momentum is along the x-axis. If we hit a 45 degree slope, half of our momentum should be converted into upward movement in y, and the other half in x. This is exactly what sine and cosine do.
Cosine tells us the percentage of our energy that we apply in x, and sine tells us the percentage of energy applied in y.
Hitting a 90 degree wall converts our horizontal momentum entirely into the y-axis and we move upward. Cosine shows that 0% of our momentum is in x, and sine shows that 100% is in y.
This is how trigonometry lets us walk on slopes.
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