Фото: Majid Asgaripour / WANA (West Asia News Agency) via Reuters
sRGB↔XYZ conversionBy Michał ‘mina86’ NazarewiczUpdated on 21st of March 2021Share on BlueskyIn an earlier post, I’ve shown how to calculate an RGB↔XYZ conversion matrix. It’s only natural to follow up with a code for converting between sRGB and XYZ colour spaces. While the matrix is a significant portion of the algorithm, there is one more step necessary: gamma correction.What is gamma correction?Human perception of light’s brightness approximates a power function of its intensity. This can be expressed as \(P = S^\alpha\) where \(P\) is the perceived brightness and \(S\) is linear intensity. \(\alpha\) has been experimentally measured to be less than one which means that people are more sensitive to changes to dark colours rather than to bright ones.Based on that observation, colour space’s encoding can be made more efficient by using higher precision when encoding dark colours and lower when encoding bright ones. This is akin to precision of floating-point numbers scaling with value’s magnitude. In RGB systems, the role of precision scaling is done by gamma correction. When colour is captured (for example from a digital camera) it goes through gamma compression which spaces dark colours apart and packs lighter colours more densely. When displaying an image, the opposite happens and encoded value goes through gamma expansion.1.00.90.80.70.60.50.40.30.20.10.0EncodedIntensityMany RGB systems use a simple \(S = E^\gamma\) expansion formula, where \(E\) is the encoded (or non-linear) value. With decoding \(\gamma\) approximating \(1/\alpha\), equal steps in encoding space correspond roughly to equal steps in perceived brightness. Image on the right demonstrates this by comparing two colour gradients. The first one has been generated by increasing encoded value in equal steps and the second one has been created by doing the same to light intensity. The former includes many dark colours while the latter contains a sudden jump in brightness from black to the next colour.sRGB uses slightly more complicated formula stitching together two functions: $$ \begin{align} E &= \begin{cases} 12.92 × S & \text{if } S ≤ S_0 \\ 1.055 × S^{1/2.4} - 0.055 & \text{otherwise} \end{cases} \\[.5em] S &= \begin{cases} {E \over 12.92} & \text{if } E ≤ E_0 \\ \left({E + 0.055 \over 1.055}\right)^{2.4} & \text{otherwise} \end{cases} \\[.5em] S_0 &= 0.00313066844250060782371 \\ E_0 &= 12.92 × S_0 \\ &= 0.04044823627710785308233 \end{align} $$The formulæ assume values are normalised to [0, 1] range. This is not always how they are expressed so a scaling step might be necessary.sRGB encodingMost common sRGB encoding uses eight bits per channel which introduces a scaling step: \(E_8 = ⌊E × 255⌉\). In an actual implementation, to increase efficiency and accuracy of gamma operations, it’s best to fuse the multiplication into aforementioned formulæ. With that arguably obvious optimisation, the equations become: $$ \begin{align} E_8 &= \begin{cases} ⌊3294.6 × S⌉ & \text{if } S ≤ S_0 \\ ⌊269.025 × S^{1/2.4} - 14.025⌉ & \text{otherwise} \end{cases} \\[.5em] S &= \begin{cases} {E_8 \over 3294.6} & \text{if } E_8 ≤ 10 \\ \left({E_8 + 14.025 \over 269.025}\right)^{2.4} & \text{otherwise} \end{cases} \\[.5em] S_0 &= 0.00313066844250060782371 \\ \end{align} $$This isn’t the only way to represent colours of course. For example, 10-bit colour depth changes the scaling factor to 1024; 16-bit high colour uses five bits for red and blue channels while five or six for green producing different scaling factors for different primaries; and HDTV caps the range to [16, 235]. Needless to say, correct formulæ need to be chosen based on the standard in question.The implementationAnd that’s it. Encoding, gamma correction and the conversion matrix are all the necessary pieces to get the conversion implemented. Like before, Rust programmers can take advantage of the srgb crate which implemented full conversion. However, to keep things interesting, in addition, here’s the conversion code written in TypeScript:type Tripple = [number, number, number];
，详情可参考safew官方下载
其最大亮点底盘性能，号称“刹车无感”，看来宝马还是希望在底盘架构和人机操控方面打动人心。这与其一贯的品牌形象相一致。
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As part of its big week of announcements, Apple has unveiled a new pair of M5 chips alongside two new MacBooks. The new M5 Pro and M5 Max chips will power the new MacBook Pro that was just announced today, while the new MacBook Air comes with the base M5. According to the company’s press release, the M5 Pro and M5 Max come with an “advanced GPU with Neural Accelerators and higher unified memory bandwidth for a massive increase in AI compute.”