Calculation of circumference arc lengths (simple formula)

/* Java Script for online ellipse arc length Calculator
Author: Joe Bartok
Date: 10000l/2004 *
URL: http://www.oocities.org/web_sketches/ellipse_notes/ellipse_arc_length/ellipse_arc_length.html
Arc Length of Ellipse
Scope: First quadrant, 0 <= x <= r
Semi-axis lying on the X-axis, r =?
Semi-axis lying on the Y-axis, r =?
(X1> x2)... X1 =? X2 =? (? Is the input value)
------------ Onclick = "solve_arc_length ()"------------------
/

Function solve_arc_length ()
{
VaR Pi = math. Pi
VaR rad = PI/180.
VaR f= 100000
VaR f= 10000000000

VaR A = Document. arc_length.r.value
VaR B = Document. arc_length.r.value
VaR X1 = Document. arc_length.x1.value
VaR X2 = Document. arc_length.x2.value

VaR prma1 = math. ACOs (x1/)
VaR prma2 = math. ACOs (x2/)

VaR d = (prma2-prma1)/20

VaR Y1 = math. SQRT (A * a * Math. sin (prma1) * Math. sin (prma1) + B * Math. cos (prma1) * Math. cos (prma1 ))
Document. arc_length.prma_1.value = math. Round (F * prma1)/F
Document. arc_length.y_1.value = math. Round (F * Y1)/F
Document. arc_length.ny_1.value = math. Round (F * Y1)/F

VaR y2 = math. SQRT (A * a * Math. sin (prma1 + 1 * D) * Math. sin (prma1 + 1 * D) + B * Math. cos (prma1 + 1 * D) * Math. cos (prma1 + 1 * D ))
Document. arc_length.prma_2.value = math. Round (F * (prma1 + 1 * D)/F
Document. arc_length.y_2.value = math. Round (F * Y2)/F
Document. arc_length.ny_2.value = math. Round (F * 4 * Y2)/F

VaR Y3 = math. SQRT (A * a * Math. sin (prma1 + 2 * D) * Math. sin (prma1 + 2 * D) + B * Math. cos (prma1 + 2 * D) * Math. cos (prma1 + 2 * D ))
Document. arc_length.prma_3.value = math. Round (F * (prma1 + 2 * D)/F
Document. arc_length.y_3.value = math. Round (F * Y3)/F
Document. arc_length.ny_3.value = math. Round (F * 2 * Y3)/F

VaR Y4 = math. SQRT (A * a * Math. sin (prma1 + 3 * D) * Math. sin (prma1 + 3 * D) + B * Math. cos (prma1 + 3 * D) * Math. cos (prma1 + 3 * D ))
Document. arc_length.prma_4.value = math. Round (F * (prma1 + 3 * D)/F
Document. arc_length.y_4.value = math. Round (F * Y4)/F
Document. arc_length.ny_4.value = math. Round (F * 4 * Y4)/F

VaR Y5 = math. SQRT (A * a * Math. sin (prma1 + 4 * D) * Math. sin (prma1 + 4 * D) + B * Math. cos (prma1 + 4 * D) * Math. cos (prma1 + 4 * D ))
Document. arc_length.prma_5.value = math. Round (F * (prma1 + 4 * D)/F
Document. arc_length.y_5.value = math. Round (F * Y5)/F
Document. arc_length.ny_5.value = math. Round (F * 2 * Y5)/F

VaR y6 = math. SQRT (A * a * Math. sin (prma1 + 5 * D) * Math. sin (prma1 + 5 * D) + B * Math. cos (prma1 + 5 * D) * Math. cos (prma1 + 5 * D ))
Document. arc_length.prma_6.value = math. Round (F * (prma1 + 5 * D)/F
Document. arc_length.y_6.value = math. Round (F * y6)/F
Document. arc_length.ny_6.value = math. Round (F * 4 * y6)/F

VaR y7 = math. SQRT (A * a * Math. sin (prma1 + 6 * D) * Math. sin (prma1 + 6 * D) + B * Math. cos (prma1 + 6 * D) * Math. cos (prma1 + 6 * D ))
Document. arc_length.prma_7.value = math. Round (F * (prma1 + 6 * D)/F
Document. arc_length.y_7.value = math. Round (F * y7)/F
Document. arc_length.ny_7.value = math. Round (F * 2 * y7)/F

VaR Y8 = math. SQRT (A * a * Math. sin (prma1 + 7 * D) * Math. sin (prma1 + 7 * D) + B * Math. cos (prma1 + 7 * D) * Math. cos (prma1 + 7 * D ))
Document. arc_length.prma_8.value = math. Round (F * (prma1 + 7 * D)/F
Document. arc_length.y_8.value = math. Round (F * Y8)/F
Document. arc_length.ny_8.value = math. Round (F * 4 * Y8)/F

VaR y9 = math. SQRT (A * a * Math. sin (prma1 + 8 * D) * Math. sin (prma1 + 8 * D) + B * Math. cos (prma1 + 8 * D) * Math. cos (prma1 + 8 * D ))
Document. arc_length.prma_9.value = math. Round (F * (prma1 + 8 * D)/F
Document. arc_length.y_9.value = math. Round (F * y9)/F
Document. arc_length.ny_9.value = math. Round (F * 2 * y9)/F

VaR Y10 = math. SQRT (A * a * Math. sin (prma1 + 9 * D) * Math. sin (prma1 + 9 * D) + B * Math. cos (prma1 + 9 * D) * Math. cos (prma1 + 9 * D ))
Document. arc_length.prma_10.value = math. Round (F * (prma1 + 9 * D)/F
Document. arc_length.y_10.value = math. Round (F * Y10)/F
Document. arc_length.ny_10.value = math. Round (F * 4 * Y10)/F

VaR y11 = math. SQRT (A * a * Math. sin (prma1 + 10 * D) * Math. sin (prma1 + 10 * D) + B * Math. cos (prma1 + 10 * D) * Math. cos (prma1 + 10 * D ))
Document. arc_length.prma_11.value = math. Round (F * (prma1 + 10 * D)/F
Document. arc_length.y_11.value = math. Round (F * y11)/F
Document. arc_length.ny_11.value = math. Round (F * 2 * y11)/F

VaR Y12 = math. SQRT (A * a * Math. sin (prma1 + 11 * D) * Math. sin (prma1 + 11 * D) + B * Math. cos (prma1 + 11 * D) * Math. cos (prma1 + 11 * D ))
Document. arc_length.prma_12.value = math. Round (F * (prma1 + 11 * D)/F
Document. arc_length.y_12.value = math. Round (F * Y12)/F
Document. arc_length.ny_12.value = math. Round (F * 4 * Y12)/F

VaR Y13 = math. SQRT (A * a * Math. sin (prma1 + 12 * D) * Math. sin (prma1 + 12 * D) + B * Math. cos (prma1 + 12 * D) * Math. cos (prma1 + 12 * D ))
Document. arc_length.prma_13.value = math. Round (F * (prma1 + 12 * D)/F
Document. arc_length.y_13.value = math. Round (F * Y13)/F
Document. arc_length.ny_13.value = math. Round (F * 2 * Y13)/F

VaR Y14 = math. SQRT (A * a * Math. sin (prma1 + 13 * D) * Math. sin (prma1 + 13 * D) + B * Math. cos (prma1 + 13 * D) * Math. cos (prma1 + 13 * D ))
Document. arc_length.prma_14.value = math. Round (F * (prma1 + 13 * D)/F
Document. arc_length.y_14.value = math. Round (F * Y14)/F
Document. arc_length.ny_14.value = math. Round (F * 4 * Y14)/F

VaR Y15 = math. SQRT (A * a * Math. sin (prma1 + 14 * D) * Math. sin (prma1 + 14 * D) + B * Math. cos (prma1 + 14 * D) * Math. cos (prma1 + 14 * D ))
Document. arc_length.prma_15.value = math. Round (F * (prma1 + 14 * D)/F
Document. arc_length.y_15.value = math. Round (F * Y15)/F
Document. arc_length.ny_15.value = math. Round (F * 2 * Y15)/F

VaR Y16 = math. SQRT (A * a * Math. sin (prma1 + 15 * D) * Math. sin (prma1 + 15 * D) + B * Math. cos (prma1 + 15 * D) * Math. cos (prma1 + 15 * D ))
Document. arc_length.prma_16.value = math. Round (F * (prma1 + 15 * D)/F
Document. arc_length.y_16.value = math. Round (F * Y16)/F
Document. arc_length.ny_16.value = math. Round (F * 4 * Y16)/F

VaR Y17 = math. SQRT (A * a * Math. sin (prma1 + 16 * D) * Math. sin (prma1 + 16 * D) + B * Math. cos (prma1 + 16 * D) * Math. cos (prma1 + 16 * D ))
Document. arc_length.prma_17.value = math. Round (F * (prma1 + 16 * D)/F
Document. arc_length.y_17.value = math. Round (F * Y17)/F
Document. arc_length.ny_17.value = math. Round (F * 2 * Y17)/F

VaR Y18 = math. SQRT (A * a * Math. sin (prma1 + 17 * D) * Math. sin (prma1 + 17 * D) + B * Math. cos (prma1 + 17 * D) * Math. cos (prma1 + 17 * D ))
Document. arc_length.prma_18.value = math. Round (F * (prma1 + 17 * D)/F
Document. arc_length.y_18.value = math. Round (F * Y18)/F
Document. arc_length.ny_18.value = math. Round (F * 4 * Y18)/F

VaR y19 = math. SQRT (A * a * Math. sin (prma1 + 18 * D) * Math. sin (prma1 + 18 * D) + B * Math. cos (prma1 + 18 * D) * Math. cos (prma1 + 18 * D ))
Document. arc_length.prma_19.value = math. Round (F * (prma1 + 18 * D)/F
Document. arc_length.y_19.value = math. Round (F * y19)/F
Document. arc_length.ny_19.value = math. Round (F * 2 * y19)/F

VaR Y20 = math. SQRT (A * a * Math. sin (prma1 + 19 * D) * Math. sin (prma1 + 19 * D) + B * Math. cos (prma1 + 19 * D) * Math. cos (prma1 + 19 * D ))
Document. arc_length.prma_1_value = math. Round (F * (prma1 + 19 * D)/F
Document. arc_length.y_1_value = math. Round (F * Y20)/F
Document. arc_length.ny_1_value = math. Round (F * 4 * Y20)/F

VaR Y21 = math. SQRT (A * a * Math. sin (prma1 + 20 * D) * Math. sin (prma1 + 20 * D) + B * Math. cos (prma1 + 20 * D) * Math. cos (prma1 + 20 * D ))
Document. arc_length.prma_21.value = math. Round (F * (prma1 + 20 * D)/F
Document. arc_length.y_21.value = math. Round (F * Y21)/F
Document. arc_length.ny_21.value = math. Round (F * Y21)/F

VaR D_3 = D/3
VaR y_sum = 1 * Y1 + 4 * y2 + 2 * Y3 + 4 * Y4 + 2 * Y5 + 4 * y6 + 2 * y7 + 4 * Y8 + 2 * y9 + 4 * Y10 + 2 * y11 + 4 * Y12 + 2 * Y13 + 4 * Y14 + 2 * Y15 + 4 * Y16 + 2 * Y17 + 4 * Y18 + 2 * y19 + 4 * Y20 + 1 * Y21
VaR S = (D/3) * (1 * Y1 + 4 * y2 + 2 * Y3 + 4 * Y4 + 2 * Y5 + 4 * y6 + 2 * y7 + 4 * Y8 + 2 * y9 + 4 * y10 + 2 * y11 + 4 * Y12 + 2 * Y13 + 4 * Y14 + 2 * Y15 + 4 * Y16 + 2 * Y17 + 4 * Y18 + 2 * y19 + 4 * y20 + 1 * Y21)

Document. arc_length.d_3.value = math. Round (F * D_3)/F
Document. arc_length.y_sum.value = math. Round (F * y_sum)/F
Document. arc_length.prma1.value = math. Round (F * prma1)/F
Document. arc_length.prma2.value = math. Round (F * prma2)/F
Document. arc_length.d.value = math. Round (F * D)/F
Document. arc_length.arc_calc.value = math. round (F * D_3)/F + "×" + math. round (F * y_sum)/F + "=" + math. round (F * s)/F
Window. Status = "ellipse arc length =" + math. Round (F * s)/F

VaR dx = (x1-X2)/20

VaR yc1 = math. SQRT (1 + B * B * X2 * x2/(A * a * (A * A-X2 * x2 )))
VaR yc2 = math. SQRT (1 + B * B * (1 * X2 + 1 * dx) * (1 * X2 + 1 * dx) /(A * a * (A * A-(1 * X2 + 1 * dx) * (1 * X2 + 1 * dx ))))
VaR yc3 = math. SQRT (1 + B * B * (1 * X2 + 2 * dx) * (1 * X2 + 2 * dx) /(A * a * (A * A-(1 * X2 + 2 * dx) * (1 * X2 + 2 * dx ))))
VaR yc4 = math. SQRT (1 + B * B * (1 * X2 + 3 * dx) * (1 * X2 + 3 * dx) /(A * a * (A * A-(1 * X2 + 3 * dx) * (1 * X2 + 3 * dx ))))
VaR yc5 = math. SQRT (1 + B * B * (1 * X2 + 4 * dx) * (1 * X2 + 4 * dx) /(A * a * (A * A-(1 * X2 + 4 * dx) * (1 * X2 + 4 * dx ))))
VaR yc6 = math. SQRT (1 + B * B * (1 * X2 + 5 * dx) * (1 * X2 + 5 * dx) /(A * a * (A * A-(1 * X2 + 5 * dx) * (1 * X2 + 5 * dx ))))
VaR yc7 = math. SQRT (1 + B * B * (1 * X2 + 6 * dx) * (1 * X2 + 6 * dx) /(A * a * (A * A-(1 * X2 + 6 * dx) * (1 * X2 + 6 * dx ))))
VaR yc8 = math. SQRT (1 + B * B * (1 * X2 + 7 * dx) * (1 * X2 + 7 * dx) /(A * a * (A * A-(1 * X2 + 7 * dx) * (1 * X2 + 7 * dx ))))
VaR yc9 = math. SQRT (1 + B * B * (1 * X2 + 8 * dx) * (1 * X2 + 8 * dx) /(A * a * (A * A-(1 * X2 + 8 * dx) * (1 * X2 + 8 * dx ))))
VaR yc10 = math. SQRT (1 + B * B * (1 * X2 + 9 * dx) * (1 * X2 + 9 * dx) /(A * a * (A * A-(1 * X2 + 9 * dx) * (1 * X2 + 9 * dx ))))
VaR yc11 = math. SQRT (1 + B * B * (1 * X2 + 10 * dx) * (1 * X2 + 10 * dx) /(A * a * (A * A-(1 * X2 + 10 * dx) * (1 * X2 + 10 * dx ))))
VaR yc12 = math. SQRT (1 + B * B * (1 * X2 + 11 * dx) * (1 * X2 + 11 * dx) /(A * a * (A * A-(1 * X2 + 11 * dx) * (1 * X2 + 11 * dx ))))
VaR yc13 = math. SQRT (1 + B * B * (1 * X2 + 12 * dx) * (1 * X2 + 12 * dx) /(A * a * (A * A-(1 * X2 + 12 * dx) * (1 * X2 + 12 * dx ))))
VaR yc14 = math. SQRT (1 + B * B * (1 * X2 + 13 * dx) * (1 * X2 + 13 * dx) /(A * a * (A * A-(1 * X2 + 13 * dx) * (1 * X2 + 13 * dx ))))
VaR yc15 = math. SQRT (1 + B * B * (1 * X2 + 14 * dx) * (1 * X2 + 14 * dx) /(A * a * (A * A-(1 * X2 + 14 * dx) * (1 * X2 + 14 * dx ))))
VaR yc16 = math. SQRT (1 + B * B * (1 * X2 + 15 * dx) * (1 * X2 + 15 * dx) /(A * a * (A * A-(1 * X2 + 15 * dx) * (1 * X2 + 15 * dx ))))
VaR yc17 = math. SQRT (1 + B * B * (1 * X2 + 16 * dx) * (1 * X2 + 16 * dx) /(A * a * (A * A-(1 * X2 + 16 * dx) * (1 * X2 + 16 * dx ))))
VaR yc6 = math. SQRT (1 + B * B * (1 * X2 + 17 * dx) * (1 * X2 + 17 * dx) /(A * a * (A * A-(1 * X2 + 17 * dx) * (1 * X2 + 17 * dx ))))
VaR yc19 = math. SQRT (1 + B * B * (1 * X2 + 18 * dx) * (1 * X2 + 18 * dx) /(A * a * (A * A-(1 * X2 + 18 * dx) * (1 * X2 + 18 * dx ))))
VaR yc20 = math. SQRT (1 + B * B * (1 * X2 + 19 * dx) * (1 * X2 + 19 * dx) /(A * a * (A * A-(1 * X2 + 19 * dx) * (1 * X2 + 19 * dx ))))
VaR yc21 = math. SQRT (1 + B * B * (1 * X2 + 20 * dx) * (1 * X2 + 20 * dx) /(A * a * (A * A-(1 * X2 + 20 * dx) * (1 * X2 + 20 * dx ))))

VaR c_arc = (dx/3) * (1 * yc1 + 4 * yc2 + 2 * yc3 + 4 * yc4 + 2 * yc5 + 4 * yc6 + 2 * yc7 + 4 * yc8 + 2 * yc9 + 4 * yc10 + 2 * yc11 + 4 * yc12 + 2 * yc13 + 4 * yc14 + 2 * yc15 + 4 * yc16 + 2 * yc17 +
4 * yc6 + 2 * yc19 + 4 * yc20 + 1 * yc21)

Document. arc_length.c_arc.value = math. Round (F * c_arc)/F
}