4 Removed unhelpful alternative solution
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HCY could be better for your needs. According to Wikipedia's HSL and HSV page, the problem you're having with HSV -- that the same "V" with different hues doesn't correspond to human perception -- is similar with HSL, but HCY could suit your needs -- the "Y" in HCY is for "luma":

Luma is roughly similar [in lightness to the original color image], but differs somewhat at high chroma. HSL L and HSV V, by contrast, diverge substantially from perceptual lightness.

HCY is described in the Wikipedia page as "luma/chroma/hue". This page, on the other hand, appears to use the "HCY" shorthand and shows how to convert it to and from RGB.

Alternatively, if you just calculate the luminance of your result with the formula you've shown, and then divide the RGB result by that calculated luminance, the final luminance should be 1.0. Multiply that colour by your desired luminance (if it's not already 1.0) and you're all done!

HCY could be better for your needs. According to Wikipedia's HSL and HSV page, the problem you're having with HSV -- that the same "V" with different hues doesn't correspond to human perception -- is similar with HSL, but HCY could suit your needs -- the "Y" in HCY is for "luma":

Luma is roughly similar [in lightness to the original color image], but differs somewhat at high chroma. HSL L and HSV V, by contrast, diverge substantially from perceptual lightness.

HCY is described in the Wikipedia page as "luma/chroma/hue". This page, on the other hand, appears to use the "HCY" shorthand and shows how to convert it to and from RGB.

Alternatively, if you just calculate the luminance of your result with the formula you've shown, and then divide the RGB result by that calculated luminance, the final luminance should be 1.0. Multiply that colour by your desired luminance (if it's not already 1.0) and you're all done!

HCY could be better for your needs. According to Wikipedia's HSL and HSV page, the problem you're having with HSV -- that the same "V" with different hues doesn't correspond to human perception -- is similar with HSL, but HCY could suit your needs -- the "Y" in HCY is for "luma":

Luma is roughly similar [in lightness to the original color image], but differs somewhat at high chroma. HSL L and HSV V, by contrast, diverge substantially from perceptual lightness.

HCY is described in the Wikipedia page as "luma/chroma/hue". This page, on the other hand, appears to use the "HCY" shorthand and shows how to convert it to and from RGB.

3 Added alternative solution
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HCY could be better for your needs. According to Wikipedia's HSL and HSV page, the problem you're having with HSV -- that the same "V" with different hues doesn't correspond to human perception -- is similar with HSL, but HCY could suit your needs -- the "Y" in HCY is for "luma":

Luma is roughly similar [in lightness to the original color image], but differs somewhat at high chroma. HSL L and HSV V, by contrast, diverge substantially from perceptual lightness.

HCY is described in the Wikipedia page as "luma/chroma/hue". This page, on the other hand, appears to use the "HCY" shorthand and shows how to convert it to and from RGB.

Alternatively, if you just calculate the luminance of your result with the formula you've shown, and then divide the RGB result by that calculated luminance, the final luminance should be 1.0. Multiply that colour by your desired luminance (if it's not already 1.0) and you're all done!

HCY could be better for your needs. According to Wikipedia's HSL and HSV page, the problem you're having with HSV -- that the same "V" with different hues doesn't correspond to human perception -- is similar with HSL, but HCY could suit your needs -- the "Y" in HCY is for "luma":

Luma is roughly similar [in lightness to the original color image], but differs somewhat at high chroma. HSL L and HSV V, by contrast, diverge substantially from perceptual lightness.

HCY is described in the Wikipedia page as "luma/chroma/hue". This page, on the other hand, appears to use the "HCY" shorthand and shows how to convert it to and from RGB.

HCY could be better for your needs. According to Wikipedia's HSL and HSV page, the problem you're having with HSV -- that the same "V" with different hues doesn't correspond to human perception -- is similar with HSL, but HCY could suit your needs -- the "Y" in HCY is for "luma":

Luma is roughly similar [in lightness to the original color image], but differs somewhat at high chroma. HSL L and HSV V, by contrast, diverge substantially from perceptual lightness.

HCY is described in the Wikipedia page as "luma/chroma/hue". This page, on the other hand, appears to use the "HCY" shorthand and shows how to convert it to and from RGB.

Alternatively, if you just calculate the luminance of your result with the formula you've shown, and then divide the RGB result by that calculated luminance, the final luminance should be 1.0. Multiply that colour by your desired luminance (if it's not already 1.0) and you're all done!

2 Fixed link title
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HCY could be better for your needs. According to WikipediaWikipedia's HSL and HSV page's disadvantages of different colour spaces, the problem you're having with HSV -- that the same "V" with different hues doesn't correspond to human perception -- is similar with HSL, but HCY could suit your needs -- the "Y" in HCY is for "luma":

Luma is roughly similar [in lightness to the original color image], but differs somewhat at high chroma. HSL L and HSV V, by contrast, diverge substantially from perceptual lightness.

HCY is described in the Wikipedia page as "luma/chroma/hue". This page, on the other hand, appears to use the "HCY" shorthand and shows how to convert it to and from RGB.

HCY could be better for your needs. According to Wikipedia's disadvantages of different colour spaces, the problem you're having with HSV -- that the same "V" with different hues doesn't correspond to human perception -- is similar with HSL, but HCY could suit your needs -- the "Y" in HCY is for "luma":

Luma is roughly similar [in lightness to the original color image], but differs somewhat at high chroma. HSL L and HSV V, by contrast, diverge substantially from perceptual lightness.

HCY is described in the Wikipedia page as "luma/chroma/hue". This page, on the other hand, appears to use the "HCY" shorthand and shows how to convert it to and from RGB.

HCY could be better for your needs. According to Wikipedia's HSL and HSV page, the problem you're having with HSV -- that the same "V" with different hues doesn't correspond to human perception -- is similar with HSL, but HCY could suit your needs -- the "Y" in HCY is for "luma":

Luma is roughly similar [in lightness to the original color image], but differs somewhat at high chroma. HSL L and HSV V, by contrast, diverge substantially from perceptual lightness.

HCY is described in the Wikipedia page as "luma/chroma/hue". This page, on the other hand, appears to use the "HCY" shorthand and shows how to convert it to and from RGB.

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