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Merge pull request #57954 from TokageItLab/refactor-cubic-interpolate
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Implement `cubic_interpolate()` as MathFunc for refactoring
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@akien-mga
akien-mga authored Feb 13, 2022
2 parents aa069a4 + 865da09 commit 7224389
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Showing 12 changed files with 142 additions and 115 deletions.
15 changes: 15 additions & 0 deletions core/math/math_funcs.h
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Expand Up @@ -235,6 +235,21 @@ class Math {
static _ALWAYS_INLINE_ double lerp(double p_from, double p_to, double p_weight) { return p_from + (p_to - p_from) * p_weight; }
static _ALWAYS_INLINE_ float lerp(float p_from, float p_to, float p_weight) { return p_from + (p_to - p_from) * p_weight; }

static _ALWAYS_INLINE_ double cubic_interpolate(double p_from, double p_to, double p_pre, double p_post, double p_weight) {
return 0.5 *
((p_from * 2.0) +
(-p_pre + p_to) * p_weight +
(2.0 * p_pre - 5.0 * p_from + 4.0 * p_to - p_post) * (p_weight * p_weight) +
(-p_pre + 3.0 * p_from - 3.0 * p_to + p_post) * (p_weight * p_weight * p_weight));
}
static _ALWAYS_INLINE_ float cubic_interpolate(float p_from, float p_to, float p_pre, float p_post, float p_weight) {
return 0.5f *
((p_from * 2.0f) +
(-p_pre + p_to) * p_weight +
(2.0f * p_pre - 5.0f * p_from + 4.0f * p_to - p_post) * (p_weight * p_weight) +
(-p_pre + 3.0f * p_from - 3.0f * p_to + p_post) * (p_weight * p_weight * p_weight));
}

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;
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20 changes: 4 additions & 16 deletions core/math/vector2.cpp
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Expand Up @@ -153,22 +153,10 @@ Vector2 Vector2::limit_length(const real_t p_len) const {
}

Vector2 Vector2::cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, const real_t p_weight) const {
Vector2 p0 = p_pre_a;
Vector2 p1 = *this;
Vector2 p2 = p_b;
Vector2 p3 = p_post_b;

real_t t = p_weight;
real_t t2 = t * t;
real_t t3 = t2 * t;

Vector2 out;
out = 0.5f *
((p1 * 2.0f) +
(-p0 + p2) * t +
(2.0f * p0 - 5.0f * p1 + 4 * p2 - p3) * t2 +
(-p0 + 3.0f * p1 - 3.0f * p2 + p3) * t3);
return out;
Vector2 res = *this;
res.x = Math::cubic_interpolate(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight);
res.y = Math::cubic_interpolate(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight);
return res;
}

Vector2 Vector2::move_toward(const Vector2 &p_to, const real_t p_delta) const {
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21 changes: 5 additions & 16 deletions core/math/vector3.cpp
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Expand Up @@ -83,22 +83,11 @@ Vector3 Vector3::limit_length(const real_t p_len) const {
}

Vector3 Vector3::cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight) const {
Vector3 p0 = p_pre_a;
Vector3 p1 = *this;
Vector3 p2 = p_b;
Vector3 p3 = p_post_b;

real_t t = p_weight;
real_t t2 = t * t;
real_t t3 = t2 * t;

Vector3 out;
out = 0.5f *
((p1 * 2.0f) +
(-p0 + p2) * t +
(2.0f * p0 - 5.0f * p1 + 4.0f * p2 - p3) * t2 +
(-p0 + 3.0f * p1 - 3.0f * p2 + p3) * t3);
return out;
Vector3 res = *this;
res.x = Math::cubic_interpolate(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight);
res.y = Math::cubic_interpolate(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight);
res.z = Math::cubic_interpolate(res.z, p_b.z, p_pre_a.z, p_post_b.z, p_weight);
return res;
}

Vector3 Vector3::move_toward(const Vector3 &p_to, const real_t p_delta) const {
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5 changes: 5 additions & 0 deletions core/variant/variant_utility.cpp
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Expand Up @@ -231,6 +231,10 @@ struct VariantUtilityFunctions {
return Math::lerp(from, to, weight);
}

static inline double cubic_interpolate(double from, double to, double pre, double post, double weight) {
return Math::cubic_interpolate(from, to, pre, post, weight);
}

static inline double lerp_angle(double from, double to, double weight) {
return Math::lerp_angle(from, to, weight);
}
Expand Down Expand Up @@ -1204,6 +1208,7 @@ void Variant::_register_variant_utility_functions() {
FUNCBINDR(snapped, sarray("x", "step"), Variant::UTILITY_FUNC_TYPE_MATH);

FUNCBINDR(lerp, sarray("from", "to", "weight"), Variant::UTILITY_FUNC_TYPE_MATH);
FUNCBINDR(cubic_interpolate, sarray("from", "to", "pre", "post", "weight"), 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);
FUNCBINDR(range_lerp, sarray("value", "istart", "istop", "ostart", "ostop"), Variant::UTILITY_FUNC_TYPE_MATH);
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11 changes: 11 additions & 0 deletions doc/classes/@GlobalScope.xml
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Expand Up @@ -221,6 +221,17 @@
[/codeblock]
</description>
</method>
<method name="cubic_interpolate">
<return type="float" />
<argument index="0" name="from" type="float" />
<argument index="1" name="to" type="float" />
<argument index="2" name="pre" type="float" />
<argument index="3" name="post" type="float" />
<argument index="4" name="weight" type="float" />
<description>
Cubic interpolates between two values by the factor defined in [code]weight[/code] with pre and post values.
</description>
</method>
<method name="db2linear">
<return type="float" />
<argument index="0" name="db" type="float" />
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18 changes: 18 additions & 0 deletions modules/mono/glue/GodotSharp/GodotSharp/Core/Mathf.cs
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Expand Up @@ -179,6 +179,24 @@ public static real_t Cosh(real_t s)
return (real_t)Math.Cosh(s);
}

/// <summary>
/// Cubic interpolates between two values by a normalized value with pre and post values.
/// </summary>
/// <param name="from">The start value for interpolation.</param>
/// <param name="to">The destination value for interpolation.</param>
/// <param name="pre">The value which before "from" value for interpolation.</param>
/// <param name="post">The value which after "to" value for interpolation.</param>
/// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
/// <returns>The resulting value of the interpolation.</returns>
public static real_t CubicInterpolate(real_t from, real_t to, real_t pre, real_t post, real_t weight)
{
return 0.5f *
((from * 2.0f) +
(-pre + to) * weight +
(2.0f * pre - 5.0f * from + 4.0f * to - post) * (weight * weight) +
(-pre + 3.0f * from - 3.0f * to + post) * (weight * weight * weight));
}

/// <summary>
/// Converts an angle expressed in degrees to radians.
/// </summary>
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18 changes: 4 additions & 14 deletions modules/mono/glue/GodotSharp/GodotSharp/Core/Vector2.cs
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Expand Up @@ -204,20 +204,10 @@ public real_t Cross(Vector2 with)
/// <returns>The interpolated vector.</returns>
public Vector2 CubicInterpolate(Vector2 b, Vector2 preA, Vector2 postB, real_t weight)
{
Vector2 p0 = preA;
Vector2 p1 = this;
Vector2 p2 = b;
Vector2 p3 = postB;

real_t t = weight;
real_t t2 = t * t;
real_t t3 = t2 * t;

return 0.5f * (
(p1 * 2.0f) +
((-p0 + p2) * t) +
(((2.0f * p0) - (5.0f * p1) + (4 * p2) - p3) * t2) +
((-p0 + (3.0f * p1) - (3.0f * p2) + p3) * t3)
return new Vector2
(
Mathf.CubicInterpolate(x, b.x, preA.x, postB.x, weight),
Mathf.CubicInterpolate(y, b.y, preA.y, postB.y, weight)
);
}

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18 changes: 5 additions & 13 deletions modules/mono/glue/GodotSharp/GodotSharp/Core/Vector3.cs
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Expand Up @@ -195,19 +195,11 @@ public Vector3 Cross(Vector3 with)
/// <returns>The interpolated vector.</returns>
public Vector3 CubicInterpolate(Vector3 b, Vector3 preA, Vector3 postB, real_t weight)
{
Vector3 p0 = preA;
Vector3 p1 = this;
Vector3 p2 = b;
Vector3 p3 = postB;

real_t t = weight;
real_t t2 = t * t;
real_t t3 = t2 * t;

return 0.5f * (
(p1 * 2.0f) + ((-p0 + p2) * t) +
(((2.0f * p0) - (5.0f * p1) + (4f * p2) - p3) * t2) +
((-p0 + (3.0f * p1) - (3.0f * p2) + p3) * t3)
return new Vector3
(
Mathf.CubicInterpolate(x, b.x, preA.x, postB.x, weight),
Mathf.CubicInterpolate(y, b.y, preA.y, postB.y, weight),
Mathf.CubicInterpolate(z, b.z, preA.z, postB.z, weight)
);
}

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84 changes: 43 additions & 41 deletions modules/visual_script/doc_classes/VisualScriptBuiltinFunc.xml
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Expand Up @@ -96,123 +96,125 @@
<constant name="MATH_LERP" value="26" enum="BuiltinFunc">
Returns a number linearly interpolated between the first two inputs, based on the third input. Uses the formula [code]a + (a - b) * t[/code].
</constant>
<constant name="MATH_INVERSE_LERP" value="27" enum="BuiltinFunc">
<constant name="MATH_CUBIC_INTERPOLATE" value="27" enum="BuiltinFunc">
</constant>
<constant name="MATH_RANGE_LERP" value="28" enum="BuiltinFunc">
<constant name="MATH_INVERSE_LERP" value="28" enum="BuiltinFunc">
</constant>
<constant name="MATH_MOVE_TOWARD" value="29" enum="BuiltinFunc">
<constant name="MATH_RANGE_LERP" value="29" enum="BuiltinFunc">
</constant>
<constant name="MATH_MOVE_TOWARD" value="30" enum="BuiltinFunc">
Moves the number toward a value, based on the third input.
</constant>
<constant name="MATH_RANDOMIZE" value="30" enum="BuiltinFunc">
<constant name="MATH_RANDOMIZE" value="31" enum="BuiltinFunc">
Randomize the seed (or the internal state) of the random number generator. Current implementation reseeds using a number based on time.
</constant>
<constant name="MATH_RANDI" value="31" enum="BuiltinFunc">
<constant name="MATH_RANDI" value="32" enum="BuiltinFunc">
Returns a random 32 bits integer value. To obtain a random value between 0 to N (where N is smaller than 2^32 - 1), you can use it with the remainder function.
</constant>
<constant name="MATH_RANDF" value="32" enum="BuiltinFunc">
<constant name="MATH_RANDF" value="33" enum="BuiltinFunc">
Returns a random floating-point value between 0 and 1. To obtain a random value between 0 to N, you can use it with multiplication.
</constant>
<constant name="MATH_RANDI_RANGE" value="33" enum="BuiltinFunc">
<constant name="MATH_RANDI_RANGE" value="34" enum="BuiltinFunc">
Returns a random 32-bit integer value between the two inputs.
</constant>
<constant name="MATH_RANDF_RANGE" value="34" enum="BuiltinFunc">
<constant name="MATH_RANDF_RANGE" value="35" enum="BuiltinFunc">
Returns a random floating-point value between the two inputs.
</constant>
<constant name="MATH_RANDFN" value="35" enum="BuiltinFunc">
<constant name="MATH_RANDFN" value="36" enum="BuiltinFunc">
Returns a normally-distributed pseudo-random number, using Box-Muller transform with the specified mean and a standard deviation. This is also called Gaussian distribution.
</constant>
<constant name="MATH_SEED" value="36" enum="BuiltinFunc">
<constant name="MATH_SEED" value="37" enum="BuiltinFunc">
Set the seed for the random number generator.
</constant>
<constant name="MATH_RANDSEED" value="37" enum="BuiltinFunc">
<constant name="MATH_RANDSEED" value="38" enum="BuiltinFunc">
Returns a random value from the given seed, along with the new seed.
</constant>
<constant name="MATH_DEG2RAD" value="38" enum="BuiltinFunc">
<constant name="MATH_DEG2RAD" value="39" enum="BuiltinFunc">
Convert the input from degrees to radians.
</constant>
<constant name="MATH_RAD2DEG" value="39" enum="BuiltinFunc">
<constant name="MATH_RAD2DEG" value="40" enum="BuiltinFunc">
Convert the input from radians to degrees.
</constant>
<constant name="MATH_LINEAR2DB" value="40" enum="BuiltinFunc">
<constant name="MATH_LINEAR2DB" value="41" enum="BuiltinFunc">
Convert the input from linear volume to decibel volume.
</constant>
<constant name="MATH_DB2LINEAR" value="41" enum="BuiltinFunc">
<constant name="MATH_DB2LINEAR" value="42" enum="BuiltinFunc">
Convert the input from decibel volume to linear volume.
</constant>
<constant name="MATH_WRAP" value="42" enum="BuiltinFunc">
<constant name="MATH_WRAP" value="43" enum="BuiltinFunc">
</constant>
<constant name="MATH_WRAPF" value="43" enum="BuiltinFunc">
<constant name="MATH_WRAPF" value="44" enum="BuiltinFunc">
</constant>
<constant name="MATH_PINGPONG" value="44" enum="BuiltinFunc">
<constant name="MATH_PINGPONG" value="45" enum="BuiltinFunc">
Returns the [code]value[/code] wrapped between [code]0[/code] and the [code]length[/code]. If the limit is reached, the next value the function returned is decreased to the [code]0[/code] side or increased to the [code]length[/code] side (like a triangle wave). If [code]length[/code] is less than zero, it becomes positive.
</constant>
<constant name="LOGIC_MAX" value="45" enum="BuiltinFunc">
<constant name="LOGIC_MAX" value="46" enum="BuiltinFunc">
Returns the greater of the two numbers, also known as their maximum.
</constant>
<constant name="LOGIC_MIN" value="46" enum="BuiltinFunc">
<constant name="LOGIC_MIN" value="47" enum="BuiltinFunc">
Returns the lesser of the two numbers, also known as their minimum.
</constant>
<constant name="LOGIC_CLAMP" value="47" enum="BuiltinFunc">
<constant name="LOGIC_CLAMP" value="48" enum="BuiltinFunc">
Returns the input clamped inside the given range, ensuring the result is never outside it. Equivalent to [code]min(max(input, range_low), range_high)[/code].
</constant>
<constant name="LOGIC_NEAREST_PO2" value="48" enum="BuiltinFunc">
<constant name="LOGIC_NEAREST_PO2" value="49" enum="BuiltinFunc">
Returns the nearest power of 2 to the input.
</constant>
<constant name="OBJ_WEAKREF" value="49" enum="BuiltinFunc">
<constant name="OBJ_WEAKREF" value="50" enum="BuiltinFunc">
Create a [WeakRef] from the input.
</constant>
<constant name="TYPE_CONVERT" value="50" enum="BuiltinFunc">
<constant name="TYPE_CONVERT" value="51" enum="BuiltinFunc">
Convert between types.
</constant>
<constant name="TYPE_OF" value="51" enum="BuiltinFunc">
<constant name="TYPE_OF" value="52" enum="BuiltinFunc">
Returns the type of the input as an integer. Check [enum Variant.Type] for the integers that might be returned.
</constant>
<constant name="TYPE_EXISTS" value="52" enum="BuiltinFunc">
<constant name="TYPE_EXISTS" value="53" enum="BuiltinFunc">
Checks if a type is registered in the [ClassDB].
</constant>
<constant name="TEXT_CHAR" value="53" enum="BuiltinFunc">
<constant name="TEXT_CHAR" value="54" enum="BuiltinFunc">
Returns a character with the given ascii value.
</constant>
<constant name="TEXT_STR" value="54" enum="BuiltinFunc">
<constant name="TEXT_STR" value="55" enum="BuiltinFunc">
Convert the input to a string.
</constant>
<constant name="TEXT_PRINT" value="55" enum="BuiltinFunc">
<constant name="TEXT_PRINT" value="56" enum="BuiltinFunc">
Print the given string to the output window.
</constant>
<constant name="TEXT_PRINTERR" value="56" enum="BuiltinFunc">
<constant name="TEXT_PRINTERR" value="57" enum="BuiltinFunc">
Print the given string to the standard error output.
</constant>
<constant name="TEXT_PRINTRAW" value="57" enum="BuiltinFunc">
<constant name="TEXT_PRINTRAW" value="58" enum="BuiltinFunc">
Print the given string to the standard output, without adding a newline.
</constant>
<constant name="TEXT_PRINT_VERBOSE" value="58" enum="BuiltinFunc">
<constant name="TEXT_PRINT_VERBOSE" value="59" enum="BuiltinFunc">
</constant>
<constant name="VAR_TO_STR" value="59" enum="BuiltinFunc">
<constant name="VAR_TO_STR" value="60" enum="BuiltinFunc">
Serialize a [Variant] to a string.
</constant>
<constant name="STR_TO_VAR" value="60" enum="BuiltinFunc">
<constant name="STR_TO_VAR" value="61" enum="BuiltinFunc">
Deserialize a [Variant] from a string serialized using [constant VAR_TO_STR].
</constant>
<constant name="VAR_TO_BYTES" value="61" enum="BuiltinFunc">
<constant name="VAR_TO_BYTES" value="62" enum="BuiltinFunc">
Serialize a [Variant] to a [PackedByteArray].
</constant>
<constant name="BYTES_TO_VAR" value="62" enum="BuiltinFunc">
<constant name="BYTES_TO_VAR" value="63" enum="BuiltinFunc">
Deserialize a [Variant] from a [PackedByteArray] serialized using [constant VAR_TO_BYTES].
</constant>
<constant name="MATH_SMOOTHSTEP" value="63" enum="BuiltinFunc">
<constant name="MATH_SMOOTHSTEP" value="64" enum="BuiltinFunc">
Returns a number smoothly interpolated between the first two inputs, based on the third input. Similar to [constant MATH_LERP], but interpolates faster at the beginning and slower at the end. Using Hermite interpolation formula:
[codeblock]
var t = clamp((weight - from) / (to - from), 0.0, 1.0)
return t * t * (3.0 - 2.0 * t)
[/codeblock]
</constant>
<constant name="MATH_POSMOD" value="64" enum="BuiltinFunc">
<constant name="MATH_POSMOD" value="65" enum="BuiltinFunc">
</constant>
<constant name="MATH_LERP_ANGLE" value="65" enum="BuiltinFunc">
<constant name="MATH_LERP_ANGLE" value="66" enum="BuiltinFunc">
</constant>
<constant name="TEXT_ORD" value="66" enum="BuiltinFunc">
<constant name="TEXT_ORD" value="67" enum="BuiltinFunc">
</constant>
<constant name="FUNC_MAX" value="67" enum="BuiltinFunc">
<constant name="FUNC_MAX" value="68" enum="BuiltinFunc">
Represents the size of the [enum BuiltinFunc] enum.
</constant>
</constants>
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