Forward Intersection
11-17-2016, 02:39 PM (This post was last modified: 11-17-2016 02:40 PM by Eddie W. Shore.)
Post: #1
 Eddie W. Shore Senior Member Posts: 1,383 Joined: Dec 2013
Forward Intersection
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
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