learning

*A smart and interesting sorting. Suppose I have five elements: a, b, c, d, e. And I want to sort them in 7 steps: Step 1: 3 comparisons: if a > b: swap(a, b); if c > d: swap(c, d); if b > d: swap(b, d), swap(a, c)  Step 2: 2 comparisons: now I need to find the position for e in {a, b, d}: if (e < b) if (e < a) e a b d else a e b d else if (e < d) a b e d else a b d e !...

A vertex shader: //WebGL Vertex Shader uniform mat4 uMVMatrix; // Model-view matrix uniform mat4 uPMatrix; // Projection matrix uniform mat4 uNMatrix; // Normal matrix attribute vec3 aVertexPosition; // Vertex position in object space attribute vec3 aVertexNormal; // Vertex normal in object space varying vec3 vPosition; // Vertex position (camera space) varying vec3 vNormal; // Vertex normal (camera space) void main(void) { vec4 camSpacePosition = uMVMatrix * vec4(aVertexPosition, 1....

The First Derivative The first derivative is the slop of the tangent line to the function at point x. It tells if the function is increasing or decreasing. For example: $f(x) = 3x^3 - 6x^2 + 2x -1$ $\frac{df}{dx} = 9x^2 - 12x + 2$ $x=0$, $\frac{df}{dx}(0) = 2$, so the function is increasing at x = 0. $x = 1$, $\frac{df}{dx}(1) = 9 - 12 + 2 = -1$, so the function is decreasing at x = 1....

Sphere in 3-D three parameters: (r, θ, φ) $x = r \cdot sin(φ) cos(θ)$ $y = r \cdot sin(φ) sin(θ)$ $z = r \cdot cos(θ)$ Trigonometry $\cos(θ) = \frac{x}{\sqrt{x^{2} + y^{2}}}$ $\sin(θ) = \frac{y}{\sqrt{x^{2} + y^{2}}}$ $\tan(θ) = \frac{y}{x}$ arcsin/arccos/arctan is the inverse. e.g. $\tan(45^{\circ}) = 1$ $\arctan(1) = 45^{\circ}$

Each sentence takes a place in a specific moment, and aspects tell us the status of the action at that moment Past Continuous/Progressive “We were sleeping when the sea creature attacked.” Perfect “We had departed from Nantucket.” Perfect Progressive “We had been sailing three weeks.” Simple “We went to search a sea creature.” “Sea creature attacked us.” Present Continuous/Progressive “We’re preparing for their next mission.” Perfect “We have built a special submarine for the search mission....