Math notation 2 #483
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Math notation 2 #483
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Points are uppercase bold, vectors are lowercase bold, no barb.
Points are uppercase bold, vectors are lowercase bold, no barb.
Points are uppercase bold, vectors are lowercase bold, no barb.
This was referenced Apr 18, 2020
books/RayTracingInOneWeekend.html
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| along a ray. Let’s think of a ray as a function $\mathbf{P}(t) = \mathbf{A} + t \mathbf{b}$. (Note: | ||
| throughout these books, we'll use uppercase bold letters for points, and lowercase bold letters for | ||
| vectors.) Here $\mathbf{P}$ is a 3D position along a line in 3D. $\mathbf{A}$ is the ray origin and |
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I'm not sure if this note is necessary. It's a level of formalism that I question for the series
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Yeah, I'll pull it.
books/RayTracingInOneWeekend.html
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| Recall that the equation for a sphere centered at the origin of radius $R$ is $x^2 + y^2 + z^2 = | ||
| R^2$. Put another way, if a given point $(x,y,z)$ is on the sphere, then $x^2 + y^2 + z^2 = R^2$. If | ||
| the given point $(x,y,z)$ is _inside_ the sphere, then $x^2 + y^2 + z^2 < R^2$, and if a given point | ||
| $(x,y,z)$ is _outside_ the sphere, then $x^2 + y^2 + z^2 > R^2$. | ||
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| It gets uglier if the sphere center is at $(\mathbf{c}_x, \mathbf{c}_y, \mathbf{c}_z)$: | ||
| It gets uglier if the sphere center is at $(\mathbf{C}_x, \mathbf{C}_y, \mathbf{C}_z)$: |
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I don't know if we discussed this, but I think components of a vector should be stylized as scalars, i.e.
$(c_x, c_y, c_z)$
Not sure if they should be upper case or lower case: $C_x% or $c_x$
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Agreed — this is a mistake. Will fix.
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I've tried to keep the scalar components with the same case as their source. Vector components are lowercase, point components are uppercase.
books/RayTracingInOneWeekend.html
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| $$ (x-\mathbf{c}_x)^2 + (y-\mathbf{c}_y)^2 + (z-\mathbf{c}_z)^2 = R^2 $$ | ||
| $$ (x-\mathbf{C}_x)^2 + (y-\mathbf{C}_y)^2 + (z-\mathbf{C}_z)^2 = r^2 $$ |
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vector component styling
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Update math notation.