# CURVES

Tutorial: Rose Range Lite Coloring. Tutorial: Rose Range Lite Coloring Or How to Make a Basket in 19 Easy Layers Text and Images © Kerry Mitchell 2001 Introduction The Rose Range Lite (RRL) coloring formula is one of many I've written that colors the image according to how the pixel relates to a geometric figure.

Rose Curves A "rose curve" is a type of polar curve. R = cos(Nq) or r = sin(Nq), where N is the frequency of the cosine or sine function, typically an integer (e.g., 1, 2, 3, etc.). On the left are true rose curves. How to Create Concentric Circles, Ellipses, Cardioids & More Using Straight Lines and a Circle. How to Create Concentric Circles, Ellipses, Cardioids & More Using Straight Lines and a Circle Using only a circle and straight lines, it's possible to create many different curves that are quite pleasing to look at and well known mathematically.

Most of the curves that are going to be explored in this post are featured at this site, which has a program for generating them, and this site which explores some of the geometry used in creating these curves. I recommend exploring both of them if you are going to create any of the designs below. I created all of these with a pencil and a ruler, or with the free computer program Geogebra. They could be created with any tool capable of making a straight line as discussed in the previous post on creating string art. Concentric circles: Concentric circles showing 6 pentagrams of different colors: Ellipse: Cardioid: Heart composed of lines, partial concentric circles, and sections of a cardioid: Materials and Tools Making Concentric Circles Making Ellipses.

FIG. 1. Variation of the order parameter from an s -wave to a g -wave.... - Scientific Figure on ResearchGate. Figure 1 shows the variation of the superconducting order parameter, i.e. , the excitation energy gap of quasipar- ticles, from an s -wave to a g -wave, by increasing weighting parameter x from 0 to 1.

Figure 1(a) simply demon- strates an s -wave. The gap develops an anisotropy and the anisotropy grows with parameter x being increased, as shown in Fig. 1(b) when x = 0 . 3. Parametric equation. MAT 238, Professor Swift. The fish is the curve in the plane described by the parametric equations x = 3(t2 - 3), y = t3 - 3t.

The following graph shows the space curve described by the vector function r(t) = < cos(t), sin(t), 1 >. Parametric equations - Roblox Wiki. This tutorial will cover the basic notion of parametric equations, and how they apply to ROBLOX.

Be careful with some of these scripts, they may lag your computer or cause it to freeze for a few moments or minutes. Mathematical Functions and graphs In algebra, you may be familiar with how a function is described with y on one side of the equals sign, and x on the other. For example: Plotting the spirograph equations with 'gnuplot' LG #133. Universidad de Oviedo, Departamento de Química Física y Analítica, E-33006-Oviedo, Spain. [ The author had specifically requested that we keep the large font used in his article in order to match the font size of the equation images; I agreed, since the two would look disproportionate otherwise.

My apologies to anyone whose eyeballs exploded due to the rapid decompression. -- Ben ] gnuplot's internal programming capabilities are used to plot the continuous and segmented versions of the spirograph equations. The segmented version, in particular, stretches the program model and requires the emulation of internal loops and conditional sentences. A PDF version of this article is available for archiving and printing. I. Synthesis. Hans Mikelson hljmm@werewolf.net.

OidEG.html. Hyperlinks - to pre-computed examples, etc.

Create YOUR OWN Definitions with Explanations : Cycloid Trochoid Epicycloid Hypocycloid Epitrochoid Hypotrochoid Animated Examples : click on the " o " , then on the figure, and use the animation controls. cycloid trochoid epicycloid hypocycloid epitrochoid hypotrochoid You can easily create variations of the Epi.... and Hypo.... examples in the MAIN worksheet.

RETURN to MAIN. Circle, Cylinder, Sphere. In what follows are various notes and algorithms dealing with circles and spheres.

Written by Paul Bourke April 1992 OpenGL/GLUT source code demonstrating the Great Circle Definition.