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>

4 files changed, 154 insertions, 69 deletions

diff --git a/scene/2d/physics_body_2d.cpp b/scene/2d/physics_body_2d.cpp
index be619ed60d..80aa99bf5e 100644
--- a/scene/2d/physics_body_2d.cpp
+++ b/scene/2d/physics_body_2d.cpp
@@ -86,11 +86,11 @@ bool PhysicsBody2D::move_and_collide(const Vector2 &p_motion, bool p_infinite_in
 	// Restore direction of motion to be along original motion,
 	// in order to avoid sliding due to recovery,
 	// but only if collision depth is low enough to avoid tunneling.
-	real_t motion_length = p_motion.length();
-	if (motion_length > CMP_EPSILON) {
+	if (p_cancel_sliding) {
+		real_t motion_length = p_motion.length();
 		real_t precision = 0.001;
 
-		if (colliding && p_cancel_sliding) {
+		if (colliding) {
 			// Can't just use margin as a threshold because collision depth is calculated on unsafe motion,
 			// so even in normal resting cases the depth can be a bit more than the margin.
 			precision += motion_length * (r_result.collision_unsafe_fraction - r_result.collision_safe_fraction);
@@ -101,16 +101,21 @@ bool PhysicsBody2D::move_and_collide(const Vector2 &p_motion, bool p_infinite_in
 		}
 
 		if (p_cancel_sliding) {
+			// When motion is null, recovery is the resulting motion.
+			Vector2 motion_normal;
+			if (motion_length > CMP_EPSILON) {
+				motion_normal = p_motion / motion_length;
+			}
+
 			// Check depth of recovery.
-			Vector2 motion_normal = p_motion / motion_length;
-			real_t dot = r_result.motion.dot(motion_normal);
-			Vector2 recovery = r_result.motion - motion_normal * dot;
+			real_t projected_length = r_result.motion.dot(motion_normal);
+			Vector2 recovery = r_result.motion - motion_normal * projected_length;
 			real_t recovery_length = recovery.length();
 			// Fixes cases where canceling slide causes the motion to go too deep into the ground,
-			// Becauses we're only taking rest information into account and not general recovery.
+			// because we're only taking rest information into account and not general recovery.
 			if (recovery_length < (real_t)p_margin + precision) {
 				// Apply adjustment to motion.
-				r_result.motion = motion_normal * dot;
+				r_result.motion = motion_normal * projected_length;
 				r_result.remainder = p_motion - r_result.motion;
 			}
 		}
@@ -978,8 +983,9 @@ void CharacterBody2D::move_and_slide() {
 	floor_normal = Vector2();
 	floor_velocity = Vector2();
 
-	// No sliding on first attempt to keep floor motion stable when possible.
-	bool sliding_enabled = false;
+	// No sliding on first attempt to keep floor motion stable when possible,
+	// when stop on slope is enabled.
+	bool sliding_enabled = !stop_on_slope;
 	for (int iteration = 0; iteration < max_slides; ++iteration) {
 		PhysicsServer2D::MotionResult result;
 		bool found_collision = false;
@@ -1018,7 +1024,11 @@ void CharacterBody2D::move_and_slide() {
 						if (stop_on_slope) {
 							if ((body_velocity_normal + up_direction).length() < 0.01) {
 								Transform2D gt = get_global_transform();
-								gt.elements[2] -= result.motion.slide(up_direction);
+								if (result.motion.length() > margin) {
+									gt.elements[2] -= result.motion.slide(up_direction);
+								} else {
+									gt.elements[2] -= result.motion;
+								}
 								set_global_transform(gt);
 								linear_velocity = Vector2();
 								return;
@@ -1054,7 +1064,7 @@ void CharacterBody2D::move_and_slide() {
 	// Apply snap.
 	Transform2D gt = get_global_transform();
 	PhysicsServer2D::MotionResult result;
-	if (move_and_collide(snap, infinite_inertia, result, margin, false, true)) {
+	if (move_and_collide(snap, infinite_inertia, result, margin, false, true, false)) {
 		bool apply = true;
 		if (up_direction != Vector2()) {
 			if (Math::acos(result.collision_normal.dot(up_direction)) <= floor_max_angle + FLOOR_ANGLE_THRESHOLD) {
@@ -1065,9 +1075,12 @@ void CharacterBody2D::move_and_slide() {
 				if (stop_on_slope) {
 					// move and collide may stray the object a bit because of pre un-stucking,
 					// so only ensure that motion happens on floor direction in this case.
-					result.motion = up_direction * up_direction.dot(result.motion);
+					if (result.motion.length() > margin) {
+						result.motion = up_direction * up_direction.dot(result.motion);
+					} else {
+						result.motion = Vector2();
+					}
 				}
-
 			} else {
 				apply = false;
 			}
diff --git a/scene/3d/physics_body_3d.cpp b/scene/3d/physics_body_3d.cpp
index e7482d35e7..4568145458 100644
--- a/scene/3d/physics_body_3d.cpp
+++ b/scene/3d/physics_body_3d.cpp
@@ -125,11 +125,11 @@ bool PhysicsBody3D::move_and_collide(const Vector3 &p_motion, bool p_infinite_in
 	// Restore direction of motion to be along original motion,
 	// in order to avoid sliding due to recovery,
 	// but only if collision depth is low enough to avoid tunneling.
-	real_t motion_length = p_motion.length();
-	if (motion_length > CMP_EPSILON) {
-		real_t precision = CMP_EPSILON;
+	if (p_cancel_sliding) {
+		real_t motion_length = p_motion.length();
+		real_t precision = 0.001;
 
-		if (colliding && p_cancel_sliding) {
+		if (colliding) {
 			// Can't just use margin as a threshold because collision depth is calculated on unsafe motion,
 			// so even in normal resting cases the depth can be a bit more than the margin.
 			precision += motion_length * (r_result.collision_unsafe_fraction - r_result.collision_safe_fraction);
@@ -140,16 +140,21 @@ bool PhysicsBody3D::move_and_collide(const Vector3 &p_motion, bool p_infinite_in
 		}
 
 		if (p_cancel_sliding) {
+			// When motion is null, recovery is the resulting motion.
+			Vector3 motion_normal;
+			if (motion_length > CMP_EPSILON) {
+				motion_normal = p_motion / motion_length;
+			}
+
 			// Check depth of recovery.
-			Vector3 motion_normal = p_motion / motion_length;
-			real_t dot = r_result.motion.dot(motion_normal);
-			Vector3 recovery = r_result.motion - motion_normal * dot;
+			real_t projected_length = r_result.motion.dot(motion_normal);
+			Vector3 recovery = r_result.motion - motion_normal * projected_length;
 			real_t recovery_length = recovery.length();
 			// Fixes cases where canceling slide causes the motion to go too deep into the ground,
-			// Becauses we're only taking rest information into account and not general recovery.
+			// because we're only taking rest information into account and not general recovery.
 			if (recovery_length < (real_t)p_margin + precision) {
 				// Apply adjustment to motion.
-				r_result.motion = motion_normal * dot;
+				r_result.motion = motion_normal * projected_length;
 				r_result.remainder = p_motion - r_result.motion;
 			}
 		}
@@ -1012,8 +1017,9 @@ void CharacterBody3D::move_and_slide() {
 	floor_normal = Vector3();
 	floor_velocity = Vector3();
 
-	// No sliding on first attempt to keep motion stable when possible.
-	bool sliding_enabled = false;
+	// No sliding on first attempt to keep floor motion stable when possible,
+	// when stop on slope is enabled.
+	bool sliding_enabled = !stop_on_slope;
 	for (int iteration = 0; iteration < max_slides; ++iteration) {
 		PhysicsServer3D::MotionResult result;
 		bool found_collision = false;
@@ -1052,7 +1058,11 @@ void CharacterBody3D::move_and_slide() {
 						if (stop_on_slope) {
 							if ((body_velocity_normal + up_direction).length() < 0.01) {
 								Transform3D gt = get_global_transform();
-								gt.origin -= result.motion.slide(up_direction);
+								if (result.motion.length() > margin) {
+									gt.origin -= result.motion.slide(up_direction);
+								} else {
+									gt.origin -= result.motion;
+								}
 								set_global_transform(gt);
 								linear_velocity = Vector3();
 								return;
@@ -1094,7 +1104,7 @@ void CharacterBody3D::move_and_slide() {
 	// Apply snap.
 	Transform3D gt = get_global_transform();
 	PhysicsServer3D::MotionResult result;
-	if (move_and_collide(snap, infinite_inertia, result, margin, false, true)) {
+	if (move_and_collide(snap, infinite_inertia, result, margin, false, true, false)) {
 		bool apply = true;
 		if (up_direction != Vector3()) {
 			if (Math::acos(result.collision_normal.dot(up_direction)) <= floor_max_angle + FLOOR_ANGLE_THRESHOLD) {
@@ -1105,7 +1115,11 @@ void CharacterBody3D::move_and_slide() {
 				if (stop_on_slope) {
 					// move and collide may stray the object a bit because of pre un-stucking,
 					// so only ensure that motion happens on floor direction in this case.
-					result.motion = result.motion.project(up_direction);
+					if (result.motion.length() > margin) {
+						result.motion = result.motion.project(up_direction);
+					} else {
+						result.motion = Vector3();
+					}
 				}
 			} else {
 				apply = false; //snapped with floor direction, but did not snap to a floor, do not snap.
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;
+						}
 					}
 				}
 
diff --git a/servers/physics_3d/space_3d_sw.cpp b/servers/physics_3d/space_3d_sw.cpp
index eff480396d..cdae744ead 100644
--- a/servers/physics_3d/space_3d_sw.cpp
+++ b/servers/physics_3d/space_3d_sw.cpp
@@ -255,6 +255,8 @@ bool PhysicsDirectSpaceState3DSW::cast_motion(const RID &p_shape, const Transfor
 
 	bool best_first = true;
 
+	Vector3 motion_normal = p_motion.normalized();
+
 	Vector3 closest_A, closest_B;
 
 	for (int i = 0; i < amount; i++) {
@@ -270,7 +272,7 @@ bool PhysicsDirectSpaceState3DSW::cast_motion(const RID &p_shape, const Transfor
 		int shape_idx = space->intersection_query_subindex_results[i];
 
 		Vector3 point_A, point_B;
-		Vector3 sep_axis = p_motion.normalized();
+		Vector3 sep_axis = motion_normal;
 
 		Transform3D col_obj_xform = col_obj->get_transform() * col_obj->get_shape_transform(shape_idx);
 		//test initial overlap, does it collide if going all the way?
@@ -279,35 +281,47 @@ bool PhysicsDirectSpaceState3DSW::cast_motion(const RID &p_shape, const Transfor
 		}
 
 		//test initial overlap, ignore objects it's inside of.
-		sep_axis = p_motion.normalized();
+		sep_axis = motion_normal;
 
 		if (!CollisionSolver3DSW::solve_distance(shape, p_xform, col_obj->get_shape(shape_idx), col_obj_xform, point_A, point_B, aabb, &sep_axis)) {
 			continue;
 		}
 
 		//just do kinematic solving
-		real_t low = 0;
-		real_t hi = 1;
-		Vector3 mnormal = p_motion.normalized();
-
+		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 fraction = low + (hi - low) * fraction_coeff;
 
-			real_t ofs = (low + hi) * 0.5;
-
-			Vector3 sep = mnormal; //important optimization for this to work fast enough
-
-			mshape.motion = xform_inv.basis.xform(p_motion * ofs);
+			mshape.motion = xform_inv.basis.xform(p_motion * fraction);
 
 			Vector3 lA, lB;
-
+			Vector3 sep = motion_normal; //important optimization for this to work fast enough
 			bool collided = !CollisionSolver3DSW::solve_distance(&mshape, p_xform, col_obj->get_shape(shape_idx), col_obj_xform, lA, lB, aabb, &sep);
 
 			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 {
 				point_A = lA;
 				point_B = lB;
-				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;
+				}
 			}
 		}
 
@@ -902,27 +916,40 @@ bool Space3DSW::test_body_motion(Body3DSW *p_body, const Transform3D &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 fraction = low + (hi - low) * fraction_coeff;
 
-					real_t ofs = (low + hi) * 0.5;
-
-					Vector3 sep = motion_normal; //important optimization for this to work fast enough
-
-					mshape.motion = body_shape_xform_inv.basis.xform(p_motion * ofs);
+					mshape.motion = body_shape_xform_inv.basis.xform(p_motion * fraction);
 
 					Vector3 lA, lB;
-
+					Vector3 sep = motion_normal; //important optimization for this to work fast enough
 					bool collided = !CollisionSolver3DSW::solve_distance(&mshape, body_shape_xform, col_obj->get_shape(shape_idx), col_obj_xform, lA, lB, motion_aabb, &sep);
 
 					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 {
 						point_A = lA;
 						point_B = lB;
-						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;
+						}
 					}
 				}