Make move_and_slide collision detection more accurate

More accurate unsafe motion calculation
* Safe and unsafe motion are calculated by dichotomy with a limited
number of steps. It's good for performance, but on long motions that
either collide near the beginning or near the end, the result can be
very imprecise.
* Now a factor 0.25 or 0.75 is used to converge faster when this case
happens, which allows longer motions to get more accurate collision
detection.
* Makes snap collision more precise, and helps with cases where diagonal collision on the border of a platform can lead to the character being stuck.

Additional improvements to move_and_slide:
* Handle slide canceling in move_and_collide with 0 velocity instead of
not applying it.
* Better handling of snap with custom logic to cancel sliding.
* Remove small jittering when using stop on slope, by canceling the
motion completely when the resulting motion is less than margin instead
of always projecting to the up direction (in both body motion and snap).

Co-authored-by: fabriceci <fabricecipolla@gmail.com>

1 files changed, 47 insertions, 16 deletions

diff --git a/servers/physics_2d/space_2d_sw.cpp b/servers/physics_2d/space_2d_sw.cpp
index 4b123b2d46..cbde7144b7 100644
--- a/servers/physics_2d/space_2d_sw.cpp
+++ b/servers/physics_2d/space_2d_sw.cpp
@@ -283,22 +283,38 @@ bool PhysicsDirectSpaceState2DSW::cast_motion(const RID &p_shape, const Transfor
 			continue;
 		}
 
-		//just do kinematic solving
-		real_t low = 0;
-		real_t hi = 1;
 		Vector2 mnormal = p_motion.normalized();
 
+		//just do kinematic solving
+		real_t low = 0.0;
+		real_t hi = 1.0;
+		real_t fraction_coeff = 0.5;
 		for (int j = 0; j < 8; j++) { //steps should be customizable..
-
-			real_t ofs = (low + hi) * 0.5;
+			real_t fraction = low + (hi - low) * fraction_coeff;
 
 			Vector2 sep = mnormal; //important optimization for this to work fast enough
-			bool collided = CollisionSolver2DSW::solve(shape, p_xform, p_motion * ofs, col_obj->get_shape(shape_idx), col_obj_xform, Vector2(), nullptr, nullptr, &sep, p_margin);
+			bool collided = CollisionSolver2DSW::solve(shape, p_xform, p_motion * fraction, col_obj->get_shape(shape_idx), col_obj_xform, Vector2(), nullptr, nullptr, &sep, p_margin);
 
 			if (collided) {
-				hi = ofs;
+				hi = fraction;
+				if ((j == 0) || (low > 0.0)) { // Did it not collide before?
+					// When alternating or first iteration, use dichotomy.
+					fraction_coeff = 0.5;
+				} else {
+					// When colliding again, converge faster towards low fraction
+					// for more accurate results with long motions that collide near the start.
+					fraction_coeff = 0.25;
+				}
 			} else {
-				low = ofs;
+				low = fraction;
+				if ((j == 0) || (hi < 1.0)) { // Did it collide before?
+					// When alternating or first iteration, use dichotomy.
+					fraction_coeff = 0.5;
+				} else {
+					// When not colliding again, converge faster towards high fraction
+					// for more accurate results with long motions that collide near the end.
+					fraction_coeff = 0.75;
+				}
 			}
 		}
 
@@ -957,20 +973,35 @@ bool Space2DSW::test_body_motion(Body2DSW *p_body, const Transform2D &p_from, co
 				}
 
 				//just do kinematic solving
-				real_t low = 0;
-				real_t hi = 1;
-
+				real_t low = 0.0;
+				real_t hi = 1.0;
+				real_t fraction_coeff = 0.5;
 				for (int k = 0; k < 8; k++) { //steps should be customizable..
-
-					real_t ofs = (low + hi) * 0.5;
+					real_t fraction = low + (hi - low) * fraction_coeff;
 
 					Vector2 sep = motion_normal; //important optimization for this to work fast enough
-					bool collided = CollisionSolver2DSW::solve(body_shape, body_shape_xform, p_motion * ofs, against_shape, col_obj_shape_xform, Vector2(), nullptr, nullptr, &sep, 0);
+					bool collided = CollisionSolver2DSW::solve(body_shape, body_shape_xform, p_motion * fraction, against_shape, col_obj_shape_xform, Vector2(), nullptr, nullptr, &sep, 0);
 
 					if (collided) {
-						hi = ofs;
+						hi = fraction;
+						if ((k == 0) || (low > 0.0)) { // Did it not collide before?
+							// When alternating or first iteration, use dichotomy.
+							fraction_coeff = 0.5;
+						} else {
+							// When colliding again, converge faster towards low fraction
+							// for more accurate results with long motions that collide near the start.
+							fraction_coeff = 0.25;
+						}
 					} else {
-						low = ofs;
+						low = fraction;
+						if ((k == 0) || (hi < 1.0)) { // Did it collide before?
+							// When alternating or first iteration, use dichotomy.
+							fraction_coeff = 0.5;
+						} else {
+							// When not colliding again, converge faster towards high fraction
+							// for more accurate results with long motions that collide near the end.
+							fraction_coeff = 0.75;
+						}
 					}
 				}