Gradients: Checking my reasoning

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Hi Jamis,

I’ve been working my way through Chapter 10: Generalising Patterns and came up agains a problem with the gradient. When applied to a Sphere, I found that the gradient was running twice across it with a hard line at X=0 (same issue as logged here: The Ray Tracer Challenge: Gradient pattern is not a gradient

I just want to double-check my interpretation of your answer is correct.

I have an AbstractPattern class which implements the general colour_at_object method. This translates the point to pattern-space via object-space thus:

    def colour_at_object(self, obj: "AbstractObject", p: Point) -> Colour:
        # Convert point to object space
        object_point = cast(Point, obj.inverse_transform * p)

        # Convert object point to pattern space
        pattern_point = cast(Point, self.inverse_transform * object_point)

        return self.colour_at(pattern_point)

Then, in the Gradient sub-class I’m implementing the colour_at method as follows:

    def colour_at(self, p: Point) -> Colour:
        distance = cast(Colour, self.b - self.a)
        # Map pattern space from [-1, 1] to [0, 1] so pattern doesn't repeat
        multiplier = (p.x + 1) / 2

        return self.a + distance * multiplier

This seems to correctly map the returned colour so that the gradient will now work across a unit sphere (breaks the tests, mind so I’ll need to fix those) … but just want to ensure that my reasoning is sound and there’s not something I’ve missed along the way?

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Hi MarkE,

I’m the author of the thread that you linked and I’m pretty sure I tried something similar to your approach at first :slight_smile:

The problem with your solution is that you shift your whole gradient, so it won’t render as you might want.

I rendered two images, one with my (I mean, Jamis really) implementation and one with yours.
Both gradients should go from red to green.

My implementation:

gradient_shadoka
gradient_shadoka400×200 14.4 KB

Your implementation:

gradient_marke
gradient_marke400×200 13.7 KB

And it makes sense when you think about it. Plug in -1 for X and the term in your method evaluates to 0. Which means that the leftmost point is going to get mapped to exactly the middle of the gradient.

Hope this helps!

3

Ah, yes - I see your point - I need to be shifting the point rather than the gradient so I’m applying the mapping at the wrong stage.

Ah well, back to the drawing board :smiley: