Handle corner cases for curve baking

When control point and point have equal position,
the derivative is 0 vector, which cause error message in Basis::look_at().
This commit handles this case.

core/math/vector2.h

@@ -113,6 +113,7 @@ struct _NO_DISCARD_ Vector2 {
 	_FORCE_INLINE_ Vector2 cubic_interpolate_in_time(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, const real_t p_weight, const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const;
 	_FORCE_INLINE_ Vector2 bezier_interpolate(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, const real_t p_t) const;
 	_FORCE_INLINE_ Vector2 bezier_derivative(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, const real_t p_t) const;
+	_FORCE_INLINE_ Vector2 bezier_tangent(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, const real_t p_t) const;
 
 	Vector2 move_toward(const Vector2 &p_to, const real_t p_delta) const;
 
@@ -289,6 +290,21 @@ Vector2 Vector2::bezier_derivative(const Vector2 &p_control_1, const Vector2 &p_
 	return res;
 }
 
+Vector2 Vector2::bezier_tangent(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, const real_t p_t) const {
+	Vector2 res = *this;
+
+	// Handle corner cases.
+	if (Math::is_zero_approx(p_t - 0.0f) && p_control_1.is_equal_approx(res)) {
+		return (p_end - res).normalized();
+	}
+
+	if (Math::is_zero_approx(p_t - 1.0f) && p_control_2.is_equal_approx(p_end)) {
+		return (p_end - res).normalized();
+	}
+
+	return res.bezier_derivative(p_control_1, p_control_2, p_end, p_t).normalized();
+}
+
 Vector2 Vector2::direction_to(const Vector2 &p_to) const {
 	Vector2 ret(p_to.x - x, p_to.y - y);
 	ret.normalize();

core/math/vector3.h

@@ -101,6 +101,7 @@ struct _NO_DISCARD_ Vector3 {
 	_FORCE_INLINE_ Vector3 cubic_interpolate_in_time(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight, const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const;
 	_FORCE_INLINE_ Vector3 bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const;
 	_FORCE_INLINE_ Vector3 bezier_derivative(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const;
+	_FORCE_INLINE_ Vector3 bezier_tangent(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const;
 
 	Vector3 move_toward(const Vector3 &p_to, const real_t p_delta) const;
 
@@ -270,6 +271,21 @@ Vector3 Vector3::bezier_derivative(const Vector3 &p_control_1, const Vector3 &p_
 	return res;
 }
 
+Vector3 Vector3::bezier_tangent(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const {
+	Vector3 res = *this;
+
+	// Handle corner cases.
+	if (Math::is_zero_approx(p_t - 0.0f) && p_control_1.is_equal_approx(res)) {
+		return (p_end - res).normalized();
+	}
+
+	if (Math::is_zero_approx(p_t - 1.0f) && p_control_2.is_equal_approx(p_end)) {
+		return (p_end - res).normalized();
+	}
+
+	return res.bezier_derivative(p_control_1, p_control_2, p_end, p_t).normalized();
+}
+
 real_t Vector3::distance_to(const Vector3 &p_to) const {
 	return (p_to - *this).length();
 }

editor/plugins/path_3d_editor_plugin.cpp

@@ -274,13 +274,10 @@ void Path3DGizmo::redraw() {
 
 			// Fish Bone.
 			v3p.push_back(p1);
-			v3p.push_back(p1 + (side - forward) * 0.06);
+			v3p.push_back(p1 + (side - forward + up * 0.3) * 0.06);
 
 			v3p.push_back(p1);
-			v3p.push_back(p1 + (-side - forward) * 0.06);
-
-			v3p.push_back(p1);
-			v3p.push_back(p1 + up * 0.03);
+			v3p.push_back(p1 + (-side - forward + up * 0.3) * 0.06);
 		}
 
 		add_lines(v3p, path_material);

scene/resources/curve.cpp

@@ -835,19 +835,19 @@ void Curve2D::_bake() const {
 
 		// Collect positions and sample tilts and tangents for each baked points.
 		bpw[0] = points[0].position;
-		bfw[0] = points[0].position.bezier_derivative(points[0].position + points[0].out, points[1].position + points[1].in, points[1].position, 0.0).normalized();
+		bfw[0] = points[0].position.bezier_tangent(points[0].position + points[0].out, points[1].position + points[1].in, points[1].position, 0.0);
 		int pidx = 0;
 
 		for (int i = 0; i < points.size() - 1; i++) {
 			for (const KeyValue<real_t, Vector2> &E : midpoints[i]) {
 				pidx++;
 				bpw[pidx] = E.value;
-				bfw[pidx] = points[i].position.bezier_derivative(points[i].position + points[i].out, points[i + 1].position + points[i + 1].in, points[i + 1].position, E.key).normalized();
+				bfw[pidx] = points[i].position.bezier_tangent(points[i].position + points[i].out, points[i + 1].position + points[i + 1].in, points[i + 1].position, E.key);
 			}
 
 			pidx++;
 			bpw[pidx] = points[i + 1].position;
-			bfw[pidx] = points[i].position.bezier_derivative(points[i].position + points[i].out, points[i + 1].position + points[i + 1].in, points[i + 1].position, 1.0).normalized();
+			bfw[pidx] = points[i].position.bezier_tangent(points[i].position + points[i].out, points[i + 1].position + points[i + 1].in, points[i + 1].position, 1.0);
 		}
 
 		// Recalculate the baked distances.
@@ -1539,21 +1539,21 @@ void Curve3D::_bake() const {
 
 		// Collect positions and sample tilts and tangents for each baked points.
 		bpw[0] = points[0].position;
-		bfw[0] = points[0].position.bezier_derivative(points[0].position + points[0].out, points[1].position + points[1].in, points[1].position, 0.0).normalized();
+		bfw[0] = points[0].position.bezier_tangent(points[0].position + points[0].out, points[1].position + points[1].in, points[1].position, 0.0);
 		btw[0] = points[0].tilt;
 		int pidx = 0;
 
 		for (int i = 0; i < points.size() - 1; i++) {
 			for (const KeyValue<real_t, Vector3> &E : midpoints[i]) {
 				pidx++;
 				bpw[pidx] = E.value;
-				bfw[pidx] = points[i].position.bezier_derivative(points[i].position + points[i].out, points[i + 1].position + points[i + 1].in, points[i + 1].position, E.key).normalized();
+				bfw[pidx] = points[i].position.bezier_tangent(points[i].position + points[i].out, points[i + 1].position + points[i + 1].in, points[i + 1].position, E.key);
 				btw[pidx] = Math::lerp(points[i].tilt, points[i + 1].tilt, E.key);
 			}
 
 			pidx++;
 			bpw[pidx] = points[i + 1].position;
-			bfw[pidx] = points[i].position.bezier_derivative(points[i].position + points[i].out, points[i + 1].position + points[i + 1].in, points[i + 1].position, 1.0).normalized();
+			bfw[pidx] = points[i].position.bezier_tangent(points[i].position + points[i].out, points[i + 1].position + points[i + 1].in, points[i + 1].position, 1.0);
 			btw[pidx] = points[i + 1].tilt;
 		}