l-curves

lissajous(sX, sY, w, h, xm, ym, c2);

• Parametric equations of a lissajous curve is:
  • var posX = sX + w*Math.cos(i*(Math.PI/180)*xm);
  • var posY = sY + h*Math.sin(i*(Math.PI/180)*ym);
  • Where i is a number that increments from 0 to 360.
• sX — center of shape, X position 
• sY — center of shape, Y position
• w — width of the shape
• h — height of the shape
• xm — offset affecting x position, numerator of a frequency ratio of a sinusoidal movement
• ym — offset affecting y position, denominator of a frequency ratio of a sinusoidal movement
• cons — constant
• c2 — stroke color

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hypotrochoids

hypotrochoid(sX, sY, rad, rad2, amt, incr, c2);

Shape of hypotrochoids dependent on the rad, rad2, amt, and incr values. Example images were generated by randomizing these values. 

• sX — center of shape, X position 
• sY — center of shape, Y position
• rad — radius of a rolling circle. 
• rad2 — radius of a fixed circle. 
• amt — constant representing 1) the amount of lines drawn, and 2) the distance of a point to the center of the rolling circle. These two variables have been arbitrarily linked. These qualities could be unlinked to allow for more randomization. 
• incr — increment value related to change in position. Within the function, the period/perd (change in position) starts at zero radians and increases by incr amount until a certain number of lines are drawn.The following parametric equations are for the x, y coordinates of points on a path is wrapped in a for loop that iterates amt amount of times. 
  • var posX = sX + ((rad2 – rad) * Math.cos(perd)) + (amt * Math.cos (((rad2 – rad)/rad) * perd));
  • var posY = sY + ((rad2 – rad) * Math.sin(perd)) + (amt * Math.sin (((rad2 – rad)/rad) * perd));
• c2 — stroke color.

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Technically, this roulette is not a hypotrochoid. The correct parametric hypotrochoid formula for posY is sY + ((rad2 – rad) * Math.sin(perd)) – (amt * Math.sin (((rad2 – rad)/rad) * perd)).

epitrochoids

epitrochoid(sX, sY, rad, rad2, amt, incr, c2);

Shape of epitrochoids dependent on the rad, rad2, amt, and incr values. Example images were generated by randomizing these values. 

• sX — center of shape; X position 
• sY — center of shape; Y position
• rad — radius of a rolling circle. 
• rad2 — radius of a fixed circle. 
• amt— constant representing 1) the amount of lines drawn, and 2) the distance of a point to the center of the rolling circle. These two variables have been arbitrarily linked. These qualities could be unlinked to allow for more randomization. 
• incr — increment value related to change in position. Within the function, the period/perd (change in position) starts at zero radians and increases by incr amount until a certain number of lines are drawn.The following parametric equations are for the x, y coordinates of points on a path is wrapped in a for loop that iterates amt amount of times:
  • var posX = sX + ((rad2 – rad) * Math.cos(perd)) + (amt * Math.cos (((rad2 – rad)/rad) * perd));
  • var posY = sY + ((rad2 – rad) * Math.sin(perd)) + (amt * Math.sin (((rad2 – rad)/rad) * perd));
• c2 — stroke color.

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rosemary

rosemary(sX, sY, rad, cons);

• sX — center of shape X position 
• sY — center of shape Y position
• rad — radius of shape
• cons — constant
• Parametric equations of a rose is:
  • var posX = sX + rad * Math.sin(cons * i) * Math.cos(i);
  • var posY = sY + rad * Math.sin(cons * i) * Math.sin(i);
  • Where i is a number that increments from 0 to 360, and the cons is the constant number.
• Rosemary takes the four trigonometric portions of these equations, that is, Math.sin(cons * i) and Math.cos(i) from posX and Math.sin(cons * i) and Math.sin(i) from posY and randomizes the trigonometric functions within these segments between Math.sin, Math.cos, Math.tan, and Math.atan.
• c2 — stroke color

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updates/expansions

• Cassini Ovals [02/22]
• Rhodonea Curve [02/22]
  • Rhodonea (Cosine Variation) [04/14]
  • Rhodonea (Tangent Variation) [04/14]
• Astroid [02/22]
• Nephroid [04/13]
• Spiral of Archimedes [04/13]
• Fermat’s Spiral [04/14]
• Lituus [04/14]
• Epicycloid, Epitrochoid, Hypocycloid, Hypotrochoid [04/14]
• Cochleoid [04/15]