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Math: add Color4::premultiplied() and unpremultiplied(). 

Am I overdoing it? Most unpremultiplication code I found doesn't even
deal with treating alpha being zero correctly, while here I'm handling
also the cases of RGB channels going over alpha, and for packed
formats trying to match precision of the same done with pack()/unpack().
pull/674/head
Vladimír Vondruš 1 year ago
parent
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d9c8f36675
3 changed files with 274 additions and 1 deletions
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  1. 3
      doc/changelog.dox
  2. 79
      src/Magnum/Math/Color.h
  3. 193
      src/Magnum/Math/Test/ColorTest.cpp

3
doc/changelog.dox
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@ -262,6 +262,9 @@ See also:
@ref Math::Color4::fromLinearRgbaInt() as counterparts to @ref Math::Color4::fromLinearRgbaInt() as counterparts to
@ref Math::Color3::fromSrgbInt(), @ref Math::Color4::fromSrgbInt() and @ref Math::Color3::fromSrgbInt(), @ref Math::Color4::fromSrgbInt() and
@ref Math::Color4::fromSrgbAlphaInt() that don't perform a sRGB conversion @ref Math::Color4::fromSrgbAlphaInt() that don't perform a sRGB conversion
- Added @ref Math::Color4::premultiplied() and
@relativeref{Math::Color4,unpremultiplied()} for converting colors to and
from premultiplied alpha representation
- New @ref Math::DualComplex::from(const Complex<T>&, const Vector2<T>&) and - New @ref Math::DualComplex::from(const Complex<T>&, const Vector2<T>&) and
@ref Math::DualQuaternion::from(const Quaternion<T>&, const Vector3<T>&) @ref Math::DualQuaternion::from(const Quaternion<T>&, const Vector3<T>&)
functions mirroring @ref Math::Matrix3::from(const Matrix2x2<T>&, const Vector2<T>&) functions mirroring @ref Math::Matrix3::from(const Matrix2x2<T>&, const Vector2<T>&)

79
src/Magnum/Math/Color.h
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@ -248,6 +248,43 @@ template<class T, typename std::enable_if<IsIntegral<T>::value, int>::type = 0>
return toXyz<typename Color3<T>::FloatingPointType>(unpack<Color3<typename Color3<T>::FloatingPointType>>(rgb)); return toXyz<typename Color3<T>::FloatingPointType>(unpack<Color3<typename Color3<T>::FloatingPointType>>(rgb));
} }
/* Alpha (un)premultiplication */
template<class T, typename std::enable_if<IsFloatingPoint<T>::value, int>::type = 0> constexpr Color4<T> premultiplied(const Color4<T>& color) {
return {color.rgb()*color.a(), color.a()};
}
template<class T, typename std::enable_if<IsIntegral<T>::value, int>::type = 0> constexpr Color4<T> premultiplied(const Color4<T>& color) {
/* The + 0.5 is to round the value to nearest integer instead of flooring.
Not using round() to have this constexpr. See premultipliedRoundtrip()
for a verification this exactly matches pack()/unpack() behavior. */
return {
T(typename Color4<T>::FloatingPointType(color.r())*color.a()/bitMax<T>() + typename Color4<T>::FloatingPointType(0.5)),
T(typename Color4<T>::FloatingPointType(color.g())*color.a()/bitMax<T>() + typename Color4<T>::FloatingPointType(0.5)),
T(typename Color4<T>::FloatingPointType(color.b())*color.a()/bitMax<T>() + typename Color4<T>::FloatingPointType(0.5)),
color.a()
};
}
template<class T, typename std::enable_if<IsFloatingPoint<T>::value, int>::type = 0> constexpr Color4<T> unpremultiplied(const Color4<T>& color) {
/* If alpha is zero, zero the RGB channels. Could keep them unchanged, but
that would add unnecessary variation to the output. */
return {color.a() == T(0) ? Color3<T>{} : color.rgb()/color.a(), color.a()};
}
template<class T, typename std::enable_if<IsIntegral<T>::value, int>::type = 0> constexpr Color4<T> unpremultiplied(const Color4<T>& color) {
/* Additionally also clamp the RGB channels so the division doesn't go over
1, as with the packed type it would result in overflow. The + 0.5 is to
round the value to nearest integer instead of flooring. Not using
round() to have this constexpr. Unlike premultiplied(), this does *not*
match pack()/unpack() behavior as this leads to better precision,
statistically speaking. See the unpremultipliedRoundtrip() test for
details. */
return color.a() == T(0) ? Color4<T>{} : Color4<T>{
T(typename Color4<T>::FloatingPointType(min(color.r(), color.a()))*bitMax<T>()/color.a() + typename Color4<T>::FloatingPointType(0.5)),
T(typename Color4<T>::FloatingPointType(min(color.g(), color.a()))*bitMax<T>()/color.a() + typename Color4<T>::FloatingPointType(0.5)),
T(typename Color4<T>::FloatingPointType(min(color.b(), color.a()))*bitMax<T>()/color.a() + typename Color4<T>::FloatingPointType(0.5)),
color.a()
};
}
/* Value for full channel (1.0f for floats, 255 for unsigned byte) */ /* Value for full channel (1.0f for floats, 255 for unsigned byte) */
#if !defined(CORRADE_MSVC2017_COMPATIBILITY) || defined(CORRADE_MSVC2015_COMPATIBILITY) #if !defined(CORRADE_MSVC2017_COMPATIBILITY) || defined(CORRADE_MSVC2015_COMPATIBILITY)
/* MSVC 2017 since 15.8 crashes with the following at a constructor line that /* MSVC 2017 since 15.8 crashes with the following at a constructor line that
@ -1204,6 +1241,48 @@ class Color4: public Vector4<T> {
return Implementation::toXyz<T>(rgb()); return Implementation::toXyz<T>(rgb());
} }
/**
* @brief Color with premultiplied alpha
* @m_since_latest
*
* The resulting color has RGB channels always less than or equal to
* alpha. Note that premultiplication isn't a reversible operation ---
* if alpha is zero, RGB channels become zero as well and
* @ref unpremultiplied() won't be able to recover the original values
* back. @f[
* \boldsymbol{c_\mathrm{premult}} = (\boldsymbol{c_{rgb}} c_a, c_a)
* @f]
*/
constexpr Color4<T> premultiplied() const {
return Implementation::premultiplied(*this);
}
/**
* @brief Color with unpremultiplied alpha
* @m_since_latest
*
* Assuming the input has premultiplied alpha, such as coming from
* @ref premultiplied(), returns an unpremultiplied color. Note that
* premultiplication isn't a reversible operation --- if alpha is zero,
* the RGB channels will be set to zero as well. @f[
* \boldsymbol{c} = \begin{cases}
* \boldsymbol{0}, & {c_\mathrm{premult}}_a = 0 \\
* (\cfrac{\boldsymbol{{c_\mathrm{premult}}_{rgb}}}{c_a}, {c_\mathrm{premult}}_a) & {c_\mathrm{premult}}_a > 0
* \end{cases}
* @f]
*
* Additionally, with packed types such as @ref Color4ub, RGB channels
* are clamped to avoid overflow: @f[
* \boldsymbol{c} = \begin{cases}
* \boldsymbol{0}, & {c_\mathrm{premult}}_a = 0 \\
* (\cfrac{\min(\boldsymbol{{c_\mathrm{premult}}_{rgb}}, {c_\mathrm{premult}}_a)}{c_a}, {c_\mathrm{premult}}_a) & {c_\mathrm{premult}}_a > 0
* \end{cases}
* @f]
*/
constexpr Color4<T> unpremultiplied() const {
return Implementation::unpremultiplied(*this);
}
/* Overloads to remove WTF-factor from return types */ /* Overloads to remove WTF-factor from return types */
#ifndef DOXYGEN_GENERATING_OUTPUT #ifndef DOXYGEN_GENERATING_OUTPUT
Color3<T>& xyz() { return Color3<T>::from(Vector4<T>::data()); } Color3<T>& xyz() { return Color3<T>::from(Vector4<T>::data()); }

193
src/Magnum/Math/Test/ColorTest.cpp
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@ -128,6 +128,11 @@ struct ColorTest: TestSuite::Tester {
void fromXyzDefaultAlpha(); void fromXyzDefaultAlpha();
void xyY(); void xyY();
void premultiplied();
template<class T> void premultipliedRoundtrip();
void unpremultiplied();
template<class T> void unpremultipliedRoundtrip();
void multiplyDivideIntegral(); void multiplyDivideIntegral();
void strictWeakOrdering(); void strictWeakOrdering();
@ -173,6 +178,15 @@ using Magnum::Deg;
using namespace Literals; using namespace Literals;
const struct {
Int r, g, b;
} UnpremultipliedRoundtripData[]{
{10, 8, 2}, /* same as in premultipliedRoundtrip() */
{4, 5, 0},
{9, 6, 7},
/** @todo for 1 and 3 it results in less precision, what to do? */
};
#if defined(CORRADE_TARGET_UNIX) || (defined(CORRADE_TARGET_WINDOWS) && !defined(CORRADE_TARGET_WINDOWS_RT)) || defined(CORRADE_TARGET_EMSCRIPTEN) #if defined(CORRADE_TARGET_UNIX) || (defined(CORRADE_TARGET_WINDOWS) && !defined(CORRADE_TARGET_WINDOWS_RT)) || defined(CORRADE_TARGET_EMSCRIPTEN)
const struct { const struct {
const char* name; const char* name;
@ -261,7 +275,17 @@ ColorTest::ColorTest() {
&ColorTest::fromXyzDefaultAlpha, &ColorTest::fromXyzDefaultAlpha,
&ColorTest::xyY, &ColorTest::xyY,
&ColorTest::multiplyDivideIntegral, &ColorTest::premultiplied,
&ColorTest::premultipliedRoundtrip<UnsignedByte>,
&ColorTest::premultipliedRoundtrip<UnsignedShort>,
&ColorTest::unpremultiplied});
addInstancedTests<ColorTest>({
&ColorTest::unpremultipliedRoundtrip<UnsignedByte>,
&ColorTest::unpremultipliedRoundtrip<UnsignedShort>},
Containers::arraySize(UnpremultipliedRoundtripData));
addTests({&ColorTest::multiplyDivideIntegral,
&ColorTest::strictWeakOrdering, &ColorTest::strictWeakOrdering,
@ -1159,6 +1183,173 @@ void ColorTest::xyY() {
CORRADE_COMPARE(xyYToXyz(xyY), xyz); CORRADE_COMPARE(xyYToXyz(xyY), xyz);
} }
void ColorTest::premultiplied() {
/* Usual scenario */
CORRADE_COMPARE((Color4{0.6f, 0.8f, 0.4f, 0.25f}).premultiplied(), (Color4{0.15f, 0.2f, 0.1f, 0.25f}));
/* Slight imprecision with packed types */
CORRADE_COMPARE((Color4us{0x9999, 0xcccc, 0x6666, 0x3fff}).premultiplied(), (Color4us{0x2666, 0x3332, 0x1999, 0x3fff}));
/* Lol it wants to treat _rgba.premultiplied() as a literal suffix as a
whole?! Load-bearing space?! */
CORRADE_COMPARE(0x99cc663f_rgba .premultiplied(), 0x2632193f_rgba);
/* Zero alpha just zeroes out the rest, no special treatment */
CORRADE_COMPARE((Color4{0.6f, 0.8f, 0.4f, 0.0f}).premultiplied(), (Color4{0.0f, 0.0f, 0.0f, 0.0f}));
CORRADE_COMPARE((Color4us{0, 0, 0, 0}).premultiplied(), (Color4us{0, 0, 0, 0}));
CORRADE_COMPARE(0x00000000_rgba .premultiplied(), 0x00000000_rgba);
/* RGB channels over 1 aren't treated in any special way */
CORRADE_COMPARE((Color4{1.6f, 1.8f, 1.4f, 0.25f}).premultiplied(), (Color4{0.4f, 0.45f, 0.35f, 0.25f}));
/* (no way to express this with packed types) */
constexpr Color4 a{0.6f, 0.8f, 0.4f, 0.25f};
constexpr Color4 ap = a.premultiplied();
CORRADE_COMPARE(ap, (Color4{0.15f, 0.2f, 0.1f, 0.25f}));
constexpr Color4us b{0x9999, 0xcccc, 0x6666, 0x3fff};
constexpr Color4us bp = b.premultiplied();
CORRADE_COMPARE(bp, (Color4us{0x2666, 0x3332, 0x1999, 0x3fff}));
constexpr Color4ub c = 0x99cc663f_rgba;
constexpr Color4ub cp = c.premultiplied();
CORRADE_COMPARE(cp, 0x2632193f_rgba);
}
template<class T> void ColorTest::premultipliedRoundtrip() {
setTestCaseTemplateName(TypeTraits<T>::name());
/* Unpacking, premultiplying and packing a color should give the same
result as premultiplying a packed color directly. The implementation
doesn't use pack() etc to be constexpr so verify the two have the same
rounding behavior.
This only holds for premultiplied(), with unpremultiplied() it doesn't,
see unpremultipliedRoundtrip() below. */
for(UnsignedInt i = 0; i != Implementation::bitMax<T>(); ++i) {
CORRADE_ITERATION(Debug::hex << i);
Math::Color4<T> a{
Math::pack<T>(1.0f), /* 0xff or 0xffff */
Math::pack<T>(0.8f), /* 0x99 or 0x9999 */
Math::pack<T>(0.2f), /* 0x33 or 0x3333 */
T(i)};
CORRADE_COMPARE(a.premultiplied(), Math::pack<Math::Color4<T>>(Math::unpack<Color4>(a).premultiplied()));
}
}
void ColorTest::unpremultiplied() {
/* Usual scenario, inverse of the above */
CORRADE_COMPARE((Color4{0.15f, 0.2f, 0.1f, 0.25f}).unpremultiplied(), (Color4{0.6f, 0.8f, 0.4f, 0.25f}));
/* Slight imprecision with packed types */
CORRADE_COMPARE((Color4us{0x2666, 0x3333, 0x1999, 0x3fff}).unpremultiplied(), (Color4us{0x999a, 0xccce, 0x6665, 0x3fff}));
/* Lol a load-bearing space again */
CORRADE_COMPARE(0x2633193f_rgba .unpremultiplied(), 0x9ace653f_rgba);
/* With zero alpha the RGB channels get ignored, no matter what they are */
CORRADE_COMPARE((Color4{0.6f, 0.8f, 0.4f, 0.0f}).unpremultiplied(), (Color4{0.0f, 0.0f, 0.0f, 0.0f}));
CORRADE_COMPARE((Color4us{0x6666, 0xcccc, 0xffff, 0}).unpremultiplied(), (Color4us{0, 0, 0, 0}));
CORRADE_COMPARE(0x33ff9900_rgba .unpremultiplied(), 0x00000000_rgba);
/* RGB channels over alpha aren't treated in any special way for floats
(inverse of what's tested in premultiplied()) */
CORRADE_COMPARE((Color4{0.4f, 0.45f, 0.35f, 0.25f}).unpremultiplied(), (Color4{1.6f, 1.8f, 1.4f, 0.25f}));
/* For packed types they get individually clamped -- i.e., it's not all of
them being set to full channel, only those that overflow */
CORRADE_COMPARE((Color4us{0x6666, 0x2666, 0x4000, 0x3fff}).unpremultiplied(), (Color4us{0xffff, 0x999a, 0xffff, 0x3fff}));
CORRADE_COMPARE(0x2666193f_rgba .unpremultiplied(), 0x9aff653f_rgba);
constexpr Color4 ap{0.15f, 0.2f, 0.1f, 0.25f};
constexpr Color4 apz{0.15f, 0.2f, 0.1f, 0.0f};
constexpr Color4 a = ap.unpremultiplied();
constexpr Color4 az = apz.unpremultiplied();
CORRADE_COMPARE(a, (Color4{0.6f, 0.8f, 0.4f, 0.25f}));
CORRADE_COMPARE(az, (Color4{0.0f, 0.0f, 0.0f, 0.0f}));
/* Second channel overflows here */
constexpr Color4us bp{0x2666, 0x6666, 0x1999, 0x3fff};
constexpr Color4us bpz{0x2666, 0x6666, 0x1999, 0};
constexpr Color4us b = bp.unpremultiplied();
constexpr Color4us bz = bpz.unpremultiplied();
CORRADE_COMPARE(b, (Color4us{0x999a, 0xffff, 0x6665, 0x3fff}));
CORRADE_COMPARE(bz, (Color4us{0, 0, 0, 0}));
/* First channel overflows here */
constexpr Color4ub cp = 0x6633193f_rgba;
constexpr Color4ub cpz = 0x66331900_rgba;
constexpr Color4ub c = cp.unpremultiplied();
constexpr Color4ub cz = cpz.unpremultiplied();
CORRADE_COMPARE(c, 0xffce653f_rgba);
CORRADE_COMPARE(cz, 0x00000000_rgba);
}
/* A variant of packed unpremultiplied() that does a calculation that has
exactly the same rounding behavior as unpack() followed by pack(). */
template<class T> constexpr Math::Color4<T> unpremultipliedPackedExact(const Math::Color4<T>& color) {
return color.a() == T(0) ? Math::Color4<T>{} : Math::Color4<T>{
T(Implementation::bitMax<T>()*((typename Math::Color4<T>::FloatingPointType(min(color.r(), color.a()))/Implementation::bitMax<T>())/(typename Math::Color4<T>::FloatingPointType(color.a())/Implementation::bitMax<T>())) + typename Math::Color4<T>::FloatingPointType(0.5)),
T(Implementation::bitMax<T>()*((typename Math::Color4<T>::FloatingPointType(min(color.g(), color.a()))/Implementation::bitMax<T>())/(typename Math::Color4<T>::FloatingPointType(color.a())/Implementation::bitMax<T>())) + typename Math::Color4<T>::FloatingPointType(0.5)),
T(Implementation::bitMax<T>()*((typename Math::Color4<T>::FloatingPointType(min(color.b(), color.a()))/Implementation::bitMax<T>())/(typename Math::Color4<T>::FloatingPointType(color.a())/Implementation::bitMax<T>())) + typename Math::Color4<T>::FloatingPointType(0.5)),
color.a()
};
}
template<class T> void ColorTest::unpremultipliedRoundtrip() {
auto&& data = UnpremultipliedRoundtripData[testCaseInstanceId()];
setTestCaseTemplateName(TypeTraits<T>::name());
setTestCaseDescription(Utility::format("{}/10, {}/10, {}/10", data.r, data.g, data.b));
/* Compared to premultipliedRoundtrip(), the sequence of operations with
pack()/unpack() causes extra rounding differences and in general is more
complex code. The simpler sequence in unpremultiplied() doesn't lead to
more precision always, but only in majority of cases, which is what this
test tries to show. */
UnsignedInt impreciseCount = 0, preciseCount = 0;
for(UnsignedInt i = 0; i != Implementation::bitMax<T>(); ++i) {
CORRADE_ITERATION(Debug::hex << i);
Math::Color4<T> ap{T(i*data.r/10),
T(i*data.g/10),
T(i*data.b/10),
T(i)};
/* It only matches when we replicate the exact sequence of operations */
Math::Color4<T> ae = unpremultipliedPackedExact(ap);
CORRADE_COMPARE(ae, Math::pack<Math::Color4<T>>(Math::unpack<Color4>(ap).unpremultiplied()));
/* The unpremultiplied() implementation is at most off-by-one from
that. Casting, not unpacking, to a float type so we can compare with
a ±1 delta even the boundary values without overflow. */
Math::Color4<T> a = ap.unpremultiplied();
CORRADE_COMPARE_WITH(Color4{a},
Color4{Math::pack<Math::Color4<T>>(Math::unpack<Color4>(ap).unpremultiplied())},
TestSuite::Compare::around(Color4{1.0f, 1.0f}));
/* If they're different, the unpremultiplied() should be always closer
to the ideal than unpack() + pack() */
if(ae != a) {
const Color3 expected{
Float(UnsignedInt(Implementation::bitMax<T>())*data.r/10)/Implementation::bitMax<T>(),
Float(UnsignedInt(Implementation::bitMax<T>())*data.g/10)/Implementation::bitMax<T>(),
Float(UnsignedInt(Implementation::bitMax<T>())*data.b/10)/Implementation::bitMax<T>()};
const Float aDelta = (Math::unpack<Color3>(a.rgb()) - expected).dot();
const Float aeDelta = (Math::unpack<Color3>(ae.rgb()) - expected).dot();
if(aDelta > aeDelta)
++impreciseCount;
else if(aDelta < aeDelta)
++preciseCount;
}
}
if(impreciseCount > preciseCount)
CORRADE_FAIL(impreciseCount << "values out of" << Implementation::bitMax<T>() << "were less precise than the pack()/unpack() variant," << preciseCount << "were more precise.");
if(impreciseCount)
CORRADE_WARN(impreciseCount << "values out of" << Implementation::bitMax<T>() << "were less precise than the pack()/unpack() variant," << preciseCount << "were more precise.");
else if(preciseCount)
CORRADE_INFO(preciseCount << "values out of" << Implementation::bitMax<T>() << "were more precise than the pack()/unpack() variant.");
}
void ColorTest::multiplyDivideIntegral() { void ColorTest::multiplyDivideIntegral() {
typedef Math::Color3<Int> Color3i; typedef Math::Color3<Int> Color3i;
typedef Math::Color4<Int> Color4i; typedef Math::Color4<Int> Color4i;

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