Forward Intersection

[Eddie W. Shore]

Introduction

The program FORDINT calculates the third point on a triangle where the coordinates of points A (xa, xb) and B (xb, yb) are known. Also, a line towards P point is aimed from point A at angle α° and from point B at angle β°.

Formulas:

Output is point P:
xp = (xa cot β + xb cot α + (yb – ya))/(cot α + cot β)
yp = (ya cot β + yb cot α + (xa - xb))/(cot α + cot β)
γ = 180° - α - β

cot θ = 1/tan θ

Note that FORDINT will set the calculator to Degrees mode.

HP Prime Program FORDINT

Input: xa, ya, α, xb, yb, β
Output: 3 element list: {xp, yp, γ} and Degrees mode is set

Code:

EXPORT FORDINT(xa,ya,a,xb,yb,b)
BEGIN
// Forward Intersection
// 2016-11-16 EWS

LOCAL xp,yp,c;
// Degree Mode
HAngle:=1;
// Calculation
xp:=(xa*COT(b)+xb*COT(a)+(yb-ya))
/(COT(a)+COT(b));
yp:=(ya*COT(b)+yb*COT(a)+(xa-xb))
/(COT(a)+COT(b));
c:=180-a-b;
RETURN {xp,yp,c};
END;

Link to my blog entry: http://edspi31415.blogspot.com/2016/11/h...rward.html

Example:
Point A: (1000, 950), angle towards point P: 30°
Point B: (1012, 997), angle towards point P: 44°

Result:
Point P: (approximately) (1024.49237, 975.078358)
Angle γ: 106°

Source: Casio. Casio fx-FD10 Pro User’s Guide Tokyo. 2014