Title: Theory / Unimportant / CS / Algo / Graphics / Fundamentals -Shirley Marschner{ / 02 Math / 5 Curve and surfaces / parametric
Tags: récupéré examplesSwitchExample1

Name: A parametric curve
Definition: the set of point \((g_1(t),\dots,g_n(t))\) for some functions \(g_i\) fixed and \(t\) taking value in their domain
Page: 39
Chapter: 2
Section: 5.2
Example: Parametric line, circles
Intuition: A function of time, with a point taking successively every position of the curve
Denoted by: \(\mathbf p=f(t)\) with \(f:\mathbb R\to\mathbb R^2\)

Name: A parametric line
Definition: A parametric curve of the form \(\mathbf o+t(\mathbf d)\) with \(\mathbf o,\mathbf d\in\mathbb R^2\) fixed
Page: 40
Chapter: 2
Section: 5.2

Name: A parametric circle
Definition: A parametric curve of the form \(\left[\begin{array}{l}x_c+r\cos\phi\\y_c+r\sin\phi\end{array}\right]\).
Page: 40
Chapter: 2
Section: 5.2

Name: A parametric ellipse
Definition: A parametric curve of the form \(\left[\begin{array}{l}x_c+a\cos\phi\\y_c+b\sin\phi\end{array}\right]\).
Page: 40
Chapter: 2
Section: 5.2

Name: A parametric spiral
Definition: A parametric curve of the form \(\left[\begin{array}{l}x_c+a\cos\phi\\y_c+b\sin\phi\\\phi\end{array}\right]\).
Page: 40
Chapter: 2
Section: 5.7

Name: A 3D parametric surface
Definition: A function \(\mathbb R^2\to\mathbb R^3\)
Page: 40
Chapter: 2
Section: 5.7
Notation: \(\left[\begin{array}{l}x\\y\\z\end{array}\right]=\mathbf p(u,v)\)