$$ % abbreviations \gdef\inf{\infty} \gdef\w{\omega} \gdef\W{\Omega} %--- % roman variables \gdef\d{\mathrm{d}} % differential, dx \gdef\o{\mathrm{o}} % outgoing, ie w_o \gdef\i{\mathrm{i}} % incoming, ie w_i \gdef\p{\mathrm{p}} % point p %--- % differentials \gdef\dx{\d x} \gdef\dy{\d y} \gdef\dw{\d \w} \gdef\dW{\d \W} % --- % trigonometry \gdef\costheta{\cos \theta} \gdef\costhetai{\cos \theta_\i} \gdef\costhetao{\cos \theta_\o} \gdef\cosphi{\cos \phi} \gdef\sintheta{\sin \theta} \gdef\sinphi{\sin \phi} \gdef\abscostheta{\lvert \costheta \rvert} \gdef\abscosthetai{\lvert \costhetai \rvert} \gdef\abscosthetao{\lvert \costhetao \rvert} % --- % differential areas \gdef\dAperp{\d A^\perp} \gdef\dA{\d A} % --- % radiometric quantities \gdef\Li{L_\i} \gdef\Lo{L_\o} % --- % differential radiometric quantities \gdef\dE{\d E} \gdef\dLo{\d \Lo} % --- % differential angles \gdef\dtheta{\d\theta} \gdef\dTheta{\d\Theta} \gdef\dphi{\d\phi} \gdef\dPhi{\d\Phi} % --- % solid angles \gdef\wi{\w_\i} \gdef\wo{\w_\o} % --- % differential solid angles \gdef\dwi{\d\wi} \gdef\dwo{\d\wo} \gdef\domega{\d \w} \gdef\dOmega{\d \W} \gdef\domegaperp{\d\w^\perp} $$

Hello

Tangent Plane

Explicit vs Implicit Surface Let’s say that you have a surface given by $z=f(x,y)$. You want to find the tangent plane to that surface at a given point $p_0 = (x_0, y_0, z_0)$. There are two tangent plane equations to choose from. The explicit equation $$ z = f(x_0, y_0) + f_x(x_0, y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0) $$ Or the implicit equation $$ 0 = \nabla f \cdot (p - p_0 ) $$ where $p = (x, y, z)$...

November 1, 2021

Website Setup

The website source is stored (for free) using github pages at https://github.com/Kaminate/kaminate.github.io. Posts are written in .md format, and converted to static html using hugo. Initial Website Setup Create github repository I’m going to assume you’re familiar with github. To host a website on GitHub Pages, create a repository https://github.com/<username>/<username>.github.io. For me, this is https://github.com/kaminate/kaminate.github.io Install Hugo If you’re like me, you have no idea what Hugo is, but you’re following the docs to create a new hugo skeleton website in the repository directory....

January 1, 2020