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Make cubic_interpolate() consider key time in animation #63602

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Aug 22, 2022
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Make cubic_interpolate() consider key time in animation #63602

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23 changes: 23 additions & 0 deletions core/math/math_funcs.h
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Expand Up @@ -253,6 +253,29 @@ class Math {
(-p_pre + 3.0f * p_from - 3.0f * p_to + p_post) * (p_weight * p_weight * p_weight));
}

static _ALWAYS_INLINE_ double cubic_interpolate_in_time(double p_from, double p_to, double p_pre, double p_post, double p_weight,
double p_to_t, double p_pre_t, double p_post_t) {
/* Barry-Goldman method */
double t = Math::lerp(0.0, p_to_t, p_weight);
double a1 = Math::lerp(p_pre, p_from, p_pre_t == 0 ? 0.0 : (t - p_pre_t) / -p_pre_t);
double a2 = Math::lerp(p_from, p_to, p_to_t == 0 ? 0.5 : t / p_to_t);
double a3 = Math::lerp(p_to, p_post, p_post_t - p_to_t == 0 ? 1.0 : (t - p_to_t) / (p_post_t - p_to_t));
double b1 = Math::lerp(a1, a2, p_to_t - p_pre_t == 0 ? 0.0 : (t - p_pre_t) / (p_to_t - p_pre_t));
double b2 = Math::lerp(a2, a3, p_post_t == 0 ? 1.0 : t / p_post_t);
return Math::lerp(b1, b2, p_to_t == 0 ? 0.5 : t / p_to_t);
}
static _ALWAYS_INLINE_ float cubic_interpolate_in_time(float p_from, float p_to, float p_pre, float p_post, float p_weight,
float p_to_t, float p_pre_t, float p_post_t) {
/* Barry-Goldman method */
float t = Math::lerp(0.0f, p_to_t, p_weight);
float a1 = Math::lerp(p_pre, p_from, p_pre_t == 0 ? 0.0f : (t - p_pre_t) / -p_pre_t);
float a2 = Math::lerp(p_from, p_to, p_to_t == 0 ? 0.5f : t / p_to_t);
float a3 = Math::lerp(p_to, p_post, p_post_t - p_to_t == 0 ? 1.0f : (t - p_to_t) / (p_post_t - p_to_t));
float b1 = Math::lerp(a1, a2, p_to_t - p_pre_t == 0 ? 0.0f : (t - p_pre_t) / (p_to_t - p_pre_t));
float b2 = Math::lerp(a2, a3, p_post_t == 0 ? 1.0f : t / p_post_t);
return Math::lerp(b1, b2, p_to_t == 0 ? 0.5f : t / p_to_t);
}

static _ALWAYS_INLINE_ double bezier_interpolate(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);
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51 changes: 51 additions & 0 deletions core/math/quaternion.cpp
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Expand Up @@ -233,6 +233,57 @@ Quaternion Quaternion::spherical_cubic_interpolate(const Quaternion &p_b, const
return q1.slerp(q2, p_weight);
}

Quaternion Quaternion::spherical_cubic_interpolate_in_time(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &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 {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
#endif
Quaternion from_q = *this;
Quaternion pre_q = p_pre_a;
Quaternion to_q = p_b;
Quaternion post_q = p_post_b;

// Align flip phases.
from_q = Basis(from_q).get_rotation_quaternion();
pre_q = Basis(pre_q).get_rotation_quaternion();
to_q = Basis(to_q).get_rotation_quaternion();
post_q = Basis(post_q).get_rotation_quaternion();

// Flip quaternions to shortest path if necessary.
bool flip1 = signbit(from_q.dot(pre_q));
pre_q = flip1 ? -pre_q : pre_q;
bool flip2 = signbit(from_q.dot(to_q));
to_q = flip2 ? -to_q : to_q;
bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : signbit(to_q.dot(post_q));
post_q = flip3 ? -post_q : post_q;

// Calc by Expmap in from_q space.
Quaternion ln_from = Quaternion(0, 0, 0, 0);
Quaternion ln_to = (from_q.inverse() * to_q).log();
Quaternion ln_pre = (from_q.inverse() * pre_q).log();
Quaternion ln_post = (from_q.inverse() * post_q).log();
Quaternion ln = Quaternion(0, 0, 0, 0);
ln.x = Math::cubic_interpolate_in_time(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
ln.y = Math::cubic_interpolate_in_time(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
ln.z = Math::cubic_interpolate_in_time(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
Quaternion q1 = from_q * ln.exp();

// Calc by Expmap in to_q space.
ln_from = (to_q.inverse() * from_q).log();
ln_to = Quaternion(0, 0, 0, 0);
ln_pre = (to_q.inverse() * pre_q).log();
ln_post = (to_q.inverse() * post_q).log();
ln = Quaternion(0, 0, 0, 0);
ln.x = Math::cubic_interpolate_in_time(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
ln.y = Math::cubic_interpolate_in_time(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
ln.z = Math::cubic_interpolate_in_time(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
Quaternion q2 = to_q * ln.exp();

// To cancel error made by Expmap ambiguity, do blends.
return q1.slerp(q2, p_weight);
}

Quaternion::operator String() const {
return "(" + String::num_real(x, false) + ", " + String::num_real(y, false) + ", " + String::num_real(z, false) + ", " + String::num_real(w, false) + ")";
}
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1 change: 1 addition & 0 deletions core/math/quaternion.h
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Expand Up @@ -72,6 +72,7 @@ struct _NO_DISCARD_ Quaternion {
Quaternion slerp(const Quaternion &p_to, const real_t &p_weight) const;
Quaternion slerpni(const Quaternion &p_to, const real_t &p_weight) const;
Quaternion spherical_cubic_interpolate(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) const;
Quaternion spherical_cubic_interpolate_in_time(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &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;

Vector3 get_axis() const;
real_t get_angle() const;
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8 changes: 8 additions & 0 deletions core/math/vector2.h
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Expand Up @@ -114,6 +114,7 @@ struct _NO_DISCARD_ Vector2 {
_FORCE_INLINE_ Vector2 lerp(const Vector2 &p_to, const real_t p_weight) const;
_FORCE_INLINE_ Vector2 slerp(const Vector2 &p_to, const real_t p_weight) const;
_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;

Vector2 move_toward(const Vector2 &p_to, const real_t p_delta) const;
Expand Down Expand Up @@ -270,6 +271,13 @@ Vector2 Vector2::cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, c
return res;
}

Vector2 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 {
Vector2 res = *this;
res.x = Math::cubic_interpolate_in_time(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
res.y = Math::cubic_interpolate_in_time(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
return res;
}

Vector2 Vector2::bezier_interpolate(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, const real_t p_t) const {
Vector2 res = *this;

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9 changes: 9 additions & 0 deletions core/math/vector3.h
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Expand Up @@ -105,6 +105,7 @@ struct _NO_DISCARD_ Vector3 {
_FORCE_INLINE_ Vector3 lerp(const Vector3 &p_to, const real_t p_weight) const;
_FORCE_INLINE_ Vector3 slerp(const Vector3 &p_to, const real_t p_weight) const;
_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;

Vector3 move_toward(const Vector3 &p_to, const real_t p_delta) const;
Expand Down Expand Up @@ -246,6 +247,14 @@ Vector3 Vector3::cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, c
return res;
}

Vector3 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 {
Vector3 res = *this;
res.x = Math::cubic_interpolate_in_time(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
res.y = Math::cubic_interpolate_in_time(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
res.z = Math::cubic_interpolate_in_time(res.z, p_b.z, p_pre_a.z, p_post_b.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
return res;
}

Vector3 Vector3::bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const {
Vector3 res = *this;

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9 changes: 9 additions & 0 deletions core/math/vector4.cpp
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Expand Up @@ -138,6 +138,15 @@ Vector4 Vector4::cubic_interpolate(const Vector4 &p_b, const Vector4 &p_pre_a, c
return res;
}

Vector4 Vector4::cubic_interpolate_in_time(const Vector4 &p_b, const Vector4 &p_pre_a, const Vector4 &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 {
Vector4 res = *this;
res.x = Math::cubic_interpolate_in_time(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
res.y = Math::cubic_interpolate_in_time(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
res.z = Math::cubic_interpolate_in_time(res.z, p_b.z, p_pre_a.z, p_post_b.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
res.w = Math::cubic_interpolate_in_time(res.w, p_b.w, p_pre_a.w, p_post_b.w, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
return res;
}

Vector4 Vector4::posmod(const real_t p_mod) const {
return Vector4(Math::fposmod(x, p_mod), Math::fposmod(y, p_mod), Math::fposmod(z, p_mod), Math::fposmod(w, p_mod));
}
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1 change: 1 addition & 0 deletions core/math/vector4.h
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Expand Up @@ -89,6 +89,7 @@ struct _NO_DISCARD_ Vector4 {
Vector4 round() const;
Vector4 lerp(const Vector4 &p_to, const real_t p_weight) const;
Vector4 cubic_interpolate(const Vector4 &p_b, const Vector4 &p_pre_a, const Vector4 &p_post_b, const real_t p_weight) const;
Vector4 cubic_interpolate_in_time(const Vector4 &p_b, const Vector4 &p_pre_a, const Vector4 &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;

Vector4 posmod(const real_t p_mod) const;
Vector4 posmodv(const Vector4 &p_modv) const;
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4 changes: 4 additions & 0 deletions core/variant/variant_call.cpp
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Expand Up @@ -1608,6 +1608,7 @@ static void _register_variant_builtin_methods() {
bind_method(Vector2, lerp, sarray("to", "weight"), varray());
bind_method(Vector2, slerp, sarray("to", "weight"), varray());
bind_method(Vector2, cubic_interpolate, sarray("b", "pre_a", "post_b", "weight"), varray());
bind_method(Vector2, cubic_interpolate_in_time, sarray("b", "pre_a", "post_b", "weight", "b_t", "pre_a_t", "post_b_t"), varray());
bind_method(Vector2, bezier_interpolate, sarray("control_1", "control_2", "end", "t"), varray());
bind_method(Vector2, max_axis_index, sarray(), varray());
bind_method(Vector2, min_axis_index, sarray(), varray());
Expand Down Expand Up @@ -1696,6 +1697,7 @@ static void _register_variant_builtin_methods() {
bind_method(Vector3, lerp, sarray("to", "weight"), varray());
bind_method(Vector3, slerp, sarray("to", "weight"), varray());
bind_method(Vector3, cubic_interpolate, sarray("b", "pre_a", "post_b", "weight"), varray());
bind_method(Vector3, cubic_interpolate_in_time, sarray("b", "pre_a", "post_b", "weight", "b_t", "pre_a_t", "post_b_t"), varray());
bind_method(Vector3, bezier_interpolate, sarray("control_1", "control_2", "end", "t"), varray());
bind_method(Vector3, move_toward, sarray("to", "delta"), varray());
bind_method(Vector3, dot, sarray("with"), varray());
Expand Down Expand Up @@ -1738,6 +1740,7 @@ static void _register_variant_builtin_methods() {
bind_method(Vector4, round, sarray(), varray());
bind_method(Vector4, lerp, sarray("to", "weight"), varray());
bind_method(Vector4, cubic_interpolate, sarray("b", "pre_a", "post_b", "weight"), varray());
bind_method(Vector4, cubic_interpolate_in_time, sarray("b", "pre_a", "post_b", "weight", "b_t", "pre_a_t", "post_b_t"), varray());
bind_method(Vector4, posmod, sarray("mod"), varray());
bind_method(Vector4, posmodv, sarray("modv"), varray());
bind_method(Vector4, snapped, sarray("step"), varray());
Expand Down Expand Up @@ -1789,6 +1792,7 @@ static void _register_variant_builtin_methods() {
bind_method(Quaternion, slerp, sarray("to", "weight"), varray());
bind_method(Quaternion, slerpni, sarray("to", "weight"), varray());
bind_method(Quaternion, spherical_cubic_interpolate, sarray("b", "pre_a", "post_b", "weight"), varray());
bind_method(Quaternion, spherical_cubic_interpolate_in_time, sarray("b", "pre_a", "post_b", "weight", "b_t", "pre_a_t", "post_b_t"), varray());
bind_method(Quaternion, get_euler, sarray(), varray());
bind_method(Quaternion, get_axis, sarray(), varray());
bind_method(Quaternion, get_angle, sarray(), varray());
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6 changes: 6 additions & 0 deletions core/variant/variant_utility.cpp
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Expand Up @@ -367,6 +367,11 @@ struct VariantUtilityFunctions {
return Math::cubic_interpolate(from, to, pre, post, weight);
}

static inline double cubic_interpolate_in_time(double from, double to, double pre, double post, double weight,
double to_t, double pre_t, double post_t) {
return Math::cubic_interpolate_in_time(from, to, pre, post, weight, to_t, pre_t, post_t);
}

static inline double bezier_interpolate(double p_start, double p_control_1, double p_control_2, double p_end, double p_t) {
return Math::bezier_interpolate(p_start, p_control_1, p_control_2, p_end, p_t);
}
Expand Down Expand Up @@ -1414,6 +1419,7 @@ void Variant::_register_variant_utility_functions() {
FUNCBINDVR3(lerp, sarray("from", "to", "weight"), Variant::UTILITY_FUNC_TYPE_MATH);
FUNCBINDR(lerpf, sarray("from", "to", "weight"), Variant::UTILITY_FUNC_TYPE_MATH);
FUNCBINDR(cubic_interpolate, sarray("from", "to", "pre", "post", "weight"), Variant::UTILITY_FUNC_TYPE_MATH);
FUNCBINDR(cubic_interpolate_in_time, sarray("from", "to", "pre", "post", "weight", "to_t", "pre_t", "post_t"), Variant::UTILITY_FUNC_TYPE_MATH);
FUNCBINDR(bezier_interpolate, sarray("start", "control_1", "control_2", "end", "t"), Variant::UTILITY_FUNC_TYPE_MATH);
FUNCBINDR(lerp_angle, sarray("from", "to", "weight"), Variant::UTILITY_FUNC_TYPE_MATH);
FUNCBINDR(inverse_lerp, sarray("from", "to", "weight"), Variant::UTILITY_FUNC_TYPE_MATH);
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15 changes: 15 additions & 0 deletions doc/classes/@GlobalScope.xml
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Expand Up @@ -260,6 +260,21 @@
Cubic interpolates between two values by the factor defined in [param weight] with pre and post values.
</description>
</method>
<method name="cubic_interpolate_in_time">
<return type="float" />
<param index="0" name="from" type="float" />
<param index="1" name="to" type="float" />
<param index="2" name="pre" type="float" />
<param index="3" name="post" type="float" />
<param index="4" name="weight" type="float" />
<param index="5" name="to_t" type="float" />
<param index="6" name="pre_t" type="float" />
<param index="7" name="post_t" type="float" />
<description>
Cubic interpolates between two values by the factor defined in [param weight] with pre and post values.
It can perform smoother interpolation than [code]cubic_interpolate()[/code] by the time values.
</description>
</method>
<method name="db2linear">
<return type="float" />
<param index="0" name="db" type="float" />
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3 changes: 3 additions & 0 deletions doc/classes/Animation.xml
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Expand Up @@ -619,6 +619,9 @@
<constant name="INTERPOLATION_CUBIC" value="2" enum="InterpolationType">
Cubic interpolation.
</constant>
<constant name="INTERPOLATION_CUBIC_IN_TIME" value="3" enum="InterpolationType">
Cubic interpolation with uniformed time.
</constant>
<constant name="UPDATE_CONTINUOUS" value="0" enum="UpdateMode">
Update between keyframes.
</constant>
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14 changes: 14 additions & 0 deletions doc/classes/Quaternion.xml
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Expand Up @@ -171,6 +171,20 @@
Performs a spherical cubic interpolation between quaternions [param pre_a], this vector, [param b], and [param post_b], by the given amount [param weight].
</description>
</method>
<method name="spherical_cubic_interpolate_in_time" qualifiers="const">
<return type="Quaternion" />
<param index="0" name="b" type="Quaternion" />
<param index="1" name="pre_a" type="Quaternion" />
<param index="2" name="post_b" type="Quaternion" />
<param index="3" name="weight" type="float" />
<param index="4" name="b_t" type="float" />
<param index="5" name="pre_a_t" type="float" />
<param index="6" name="post_b_t" type="float" />
<description>
Performs a spherical cubic interpolation between quaternions [param pre_a], this vector, [param b], and [param post_b], by the given amount [param weight].
It can perform smoother interpolation than [code]spherical_cubic_interpolate()[/code] by the time values.
</description>
</method>
</methods>
<members>
<member name="w" type="float" setter="" getter="" default="1.0">
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14 changes: 14 additions & 0 deletions doc/classes/Vector2.xml
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Expand Up @@ -135,6 +135,20 @@
Cubically interpolates between this vector and [param b] using [param pre_a] and [param post_b] as handles, and returns the result at position [param weight]. [param weight] is on the range of 0.0 to 1.0, representing the amount of interpolation.
</description>
</method>
<method name="cubic_interpolate_in_time" qualifiers="const">
<return type="Vector2" />
<param index="0" name="b" type="Vector2" />
<param index="1" name="pre_a" type="Vector2" />
<param index="2" name="post_b" type="Vector2" />
<param index="3" name="weight" type="float" />
<param index="4" name="b_t" type="float" />
<param index="5" name="pre_a_t" type="float" />
<param index="6" name="post_b_t" type="float" />
<description>
Cubically interpolates between this vector and [param b] using [param pre_a] and [param post_b] as handles, and returns the result at position [param weight]. [param weight] is on the range of 0.0 to 1.0, representing the amount of interpolation.
It can perform smoother interpolation than [code]cubic_interpolate()[/code] by the time values.
</description>
</method>
<method name="direction_to" qualifiers="const">
<return type="Vector2" />
<param index="0" name="to" type="Vector2" />
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14 changes: 14 additions & 0 deletions doc/classes/Vector3.xml
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Performs a cubic interpolation between this vector and [param b] using [param pre_a] and [param post_b] as handles, and returns the result at position [param weight]. [param weight] is on the range of 0.0 to 1.0, representing the amount of interpolation.
</description>
</method>
<method name="cubic_interpolate_in_time" qualifiers="const">
<return type="Vector3" />
<param index="0" name="b" type="Vector3" />
<param index="1" name="pre_a" type="Vector3" />
<param index="2" name="post_b" type="Vector3" />
<param index="3" name="weight" type="float" />
<param index="4" name="b_t" type="float" />
<param index="5" name="pre_a_t" type="float" />
<param index="6" name="post_b_t" type="float" />
<description>
Performs a cubic interpolation between this vector and [param b] using [param pre_a] and [param post_b] as handles, and returns the result at position [param weight]. [param weight] is on the range of 0.0 to 1.0, representing the amount of interpolation.
It can perform smoother interpolation than [code]cubic_interpolate()[/code] by the time values.
</description>
</method>
<method name="direction_to" qualifiers="const">
<return type="Vector3" />
<param index="0" name="to" type="Vector3" />
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