The border of the color space corresponding to monochromatic colors is convex, so any triangle inscribed in that curve border will leave parts of the color space that cannot be reproduced on a display.
The convexity of the border means that if you compute the 3 coefficients of RGB colors that match a desired color, there will always be some colors that need one negative coefficient, regardless of the choice for the RGB primary colors. On any display, it is impossible to realize a negative brightness of a color, so on a RGB display there will always be some colors whose hue and brightness can be reproduced, but their saturation cannot be reproduced.
The only way to make smaller the parts of the color space that cannot be reproduced is to take more points on the monochromatic border, replacing the triangle of reproducible colors with a polygon that fits more closely the curved border.
The entire color space perceived by humans could be reproduced on a display only with tunable lasers, not with fixed-frequency primary colors. One could use fixed-frequency primary colors only if they would stimulate directly the photoreceptors in the eye, to enable workarounds for the overlapping filter characteristics of the cones and for the signal processing done in the retina.
The border of the color space corresponding to monochromatic colors is convex, so any triangle inscribed in that curve border will leave parts of the color space that cannot be reproduced on a display.
The convexity of the border means that if you compute the 3 coefficients of RGB colors that match a desired color, there will always be some colors that need one negative coefficient, regardless of the choice for the RGB primary colors. On any display, it is impossible to realize a negative brightness of a color, so on a RGB display there will always be some colors whose hue and brightness can be reproduced, but their saturation cannot be reproduced.
The only way to make smaller the parts of the color space that cannot be reproduced is to take more points on the monochromatic border, replacing the triangle of reproducible colors with a polygon that fits more closely the curved border.
The entire color space perceived by humans could be reproduced on a display only with tunable lasers, not with fixed-frequency primary colors. One could use fixed-frequency primary colors only if they would stimulate directly the photoreceptors in the eye, to enable workarounds for the overlapping filter characteristics of the cones and for the signal processing done in the retina.