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Refactor Curve3D::_bake() method

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The main change is to caculate tangent directly from bezier curve, without going
through discretized polyline, avoiding pitfalls of discretization.

Other changes are:
1. Add an bezier_derivative() method for Vector3, Vector2, and Math;
2. Add an tesselate_even_length() method to Curve3D, which tesselate bezier curve to even length segments adaptively;
3. Cache the tangent vectors in baked_tangent_vector_cache;
This commit is contained in:
Yaohua Xiong 2022-11-23 11:11:58 +08:00
parent fa270c2456
commit f9fa182abc
11 changed files with 223 additions and 130 deletions
Download patch file Download diff file Expand all files Collapse all files

20
core/math/math_funcs.h
View file

@ -364,6 +364,26 @@ public:
return p_start * omt3 + p_control_1 * omt2 * p_t * 3.0f + p_control_2 * omt * t2 * 3.0f + p_end * t3;
}
static _ALWAYS_INLINE_ double bezier_derivative(double p_start, double p_control_1, double p_control_2, double p_end, double p_t) {
/* Formula from Wikipedia article on Bezier curves. */
double omt = (1.0 - p_t);
double omt2 = omt * omt;
double t2 = p_t * p_t;
double d = (p_control_1 - p_start) * 3.0 * omt2 + (p_control_2 - p_control_1) * 6.0 * omt * p_t + (p_end - p_control_2) * 3.0 * t2;
return d;
}
static _ALWAYS_INLINE_ float bezier_derivative(float p_start, float p_control_1, float p_control_2, float p_end, float p_t) {
/* Formula from Wikipedia article on Bezier curves. */
float omt = (1.0f - p_t);
float omt2 = omt * omt;
float t2 = p_t * p_t;
float d = (p_control_1 - p_start) * 3.0f * omt2 + (p_control_2 - p_control_1) * 6.0f * omt * p_t + (p_end - p_control_2) * 3.0f * t2;
return d;
}
static _ALWAYS_INLINE_ double lerp_angle(double p_from, double p_to, double p_weight) {
double difference = fmod(p_to - p_from, Math_TAU);
double distance = fmod(2.0 * difference, Math_TAU) - difference;

13
core/math/vector2.h
View file

@ -112,6 +112,7 @@ struct _NO_DISCARD_ Vector2 {
_FORCE_INLINE_ Vector2 cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, const real_t p_weight) const;
_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;
Vector2 move_toward(const Vector2 &p_to, const real_t p_delta) const;
@ -289,6 +290,18 @@ Vector2 Vector2::bezier_interpolate(const Vector2 &p_control_1, const Vector2 &p
return res * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3;
}
Vector2 Vector2::bezier_derivative(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, const real_t p_t) const {
Vector2 res = *this;
/* Formula from Wikipedia article on Bezier curves. */
real_t omt = (1.0 - p_t);
real_t omt2 = omt * omt;
real_t t2 = p_t * p_t;
Vector2 d = (p_control_1 - res) * 3.0 * omt2 + (p_control_2 - p_control_1) * 6.0 * omt * p_t + (p_end - p_control_2) * 3.0 * t2;
return d;
}
Vector2 Vector2::direction_to(const Vector2 &p_to) const {
Vector2 ret(p_to.x - x, p_to.y - y);
ret.normalize();

13
core/math/vector3.h
View file

@ -100,6 +100,7 @@ struct _NO_DISCARD_ Vector3 {
_FORCE_INLINE_ Vector3 cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight) const;
_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;
Vector3 move_toward(const Vector3 &p_to, const real_t p_delta) const;
@ -265,6 +266,18 @@ Vector3 Vector3::bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p
return res * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3;
}
Vector3 Vector3::bezier_derivative(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const {
Vector3 res = *this;
/* Formula from Wikipedia article on Bezier curves. */
real_t omt = (1.0 - p_t);
real_t omt2 = omt * omt;
real_t t2 = p_t * p_t;
Vector3 d = (p_control_1 - res) * 3.0 * omt2 + (p_control_2 - p_control_1) * 6.0 * omt * p_t + (p_end - p_control_2) * 3.0 * t2;
return d;
}
real_t Vector3::distance_to(const Vector3 &p_to) const {
return (p_to - *this).length();
}