ImageJ Toolset for measuring (1) circumradius, (2) angle between two lines, and (3) distance between line and point.

Basic_Measurement.txt

// Measurement tools
// author j.iamsamang@tue.nl
// http://wsr.imagej.net/developer/macro/macros.html#toolsets

var obtusedAngles = false;

macro "Unused Tool - " {}

macro "X axis Registration Tool - C037T2d13-T9d13X" {
       cmd = getArgument();
}
macro "Y axis Registration Tool - C037T2d13|T9d13Y" {
       cmd = getArgument();
}

macro "circumcircle [f1]" { 
	requires("1.30k");
	if (selectionType() == -1) {
		exit("[circumcircle]: Please select three points!");
	}
	getSelectionCoordinates(x, y);
	if (x.length != 3){
		exit("Calculation requires only three points");
	}

	//-- Get pixel data
	getPixelSize(unit, pw, ph, pd);
	
	//-- First calculate the perimeter of the triangle
	d1=sqrt((x[0]-x[1])*(x[0]-x[1])*pw*pw+(y[0]-y[1])*(y[0]-y[1])*ph*ph);
	d2=sqrt((x[1]-x[2])*(x[1]-x[2])*pw*pw+(y[1]-y[2])*(y[1]-y[2])*ph*ph);
	d3=sqrt((x[2]-x[0])*(x[2]-x[0])*pw*pw+(y[2]-y[0])*(y[2]-y[0])*ph*ph);
	//-- Half the perimeter
	s=0.5*(d1+d2+d3);
	//-- Area of circumcircle
	a=sqrt(s*(s-d1)*(s-d2)*(s*d3));
	//-- Circumradius
	r=(d1*d2*d3)/sqrt((d1+d2+d3)*(d2+d3-d1)*(d3+d1-d2)*(d1+d2-d3));
	//-- Menger curvature is the inverse of the radius of the circle
	mc=1/r;
	//-- Centroid coordinates (from https://en.wikipedia.org/wiki/Circumscribed_circle#Cartesian_coordinates_2)
	D=2*abs(x[0]*(y[1]-y[2]) + x[1]*(y[2]-y[0]) + x[2]*(y[0]-y[1]));
	
	cenX=abs((x[0]*x[0]+y[0]*y[0]) * (y[1]-y[2]) + (x[1]*x[1]+y[1]*y[1]) * (y[2]-y[0]) + (x[2]*x[2]+y[2]*y[2]) * (y[0]-y[1]))/D;
	cenY=abs((x[0]*x[0]+y[0]*y[0]) * (x[2]-x[1]) + (x[1]*x[1]+y[1]*y[1]) * (x[0]-x[2]) + (x[2]*x[2]+y[2]*y[2]) * (x[1]-x[0]))/D;
	
	//-- report
	//print("a: "+x[0]+","+y[0]);
	//print("b: "+x[1]+","+y[1]);
	//print("c: "+x[2]+","+y[2]);
	//print("Area of circumcircle: "+a);
	//print("Radius: "+r);
	//print("Menger Curvature: "+mc);
	//print("Circumcentre: "+cenX+","+cenY);
	row = Table.size;	
	Table.set("Area", row, a);
	Table.set("Radius", row, r);
	Table.set("Menger Curvature", row, mc);
	Table.set("Centre X", row, cenX);
	Table.set("Centre Y", row, cenY);
	Table.update;
	
	//-- Create an overlay
	
	//-- Triangle
	makePolygon(x[0],y[0],x[1],y[1],x[2],y[2]);
	Overlay.addSelection("cyan");
	
	//-- Circumcentre
	makeLine(cenX-5,cenY,cenX+5,cenY);
	Overlay.addSelection("magenta");
	makeLine(cenX,cenY-5,cenX,cenY+5);
	Overlay.addSelection("magenta");
	
	//-- Circumcircle
	run("Specify...", "width="+(r*2/pw)+" height="+(r*2/ph)+" x="+cenX+" y="+cenY+" oval centered");
	Overlay.addSelection("red");
	run("Select None");
}

macro "Two-line Angle [f2]" {
	requires("1.30k");
	if (selectionType() == -1) {
		exit("[Two-lines Angle]: Please select four points!");
	}
	
	getSelectionCoordinates(x, y);
	if (x.length != 4) {
		exit("[Two-lines Angle]: Please select four points!");
	}
	
	m1 = (y[1]-y[0])/(x[1]-x[0]+1e-16);
	m2 = (y[3]-y[2])/(x[3]-x[2]+1e-16);
	theta_deg = 0;
	if (abs(m1*m2 + 1) < 1e-9) {
		theta_deg = 90.0;
	} else {
		tan_theta = abs((m1 - m2)/(1+m1*m2));
		theta_deg = atan2(tan_theta, 1.0) * 180.0 / PI;
	}
	if (obtusedAngles) {
		theta_deg = 180 - theta_deg;
	}
	
	makeLine(x[0],y[0],x[1],y[1]);
	Overlay.addSelection("red");
	makeLine(x[2],y[2],x[3],y[3]);
	Overlay.addSelection("red");
	
	mid1 = newArray((x[0]+x[1])/2, (y[0]+y[1])/2);
	mid2 = newArray((x[2]+x[3])/2, (y[2]+y[3])/2);
	makeSelection("polyline", newArray(mid1[0], mid2[0]), newArray(mid1[1], mid2[1]));
	setForegroundColor(0, 255, 255);
	run("Dotted Line", "line=1 dash=6,6");
	run("Select None");
	
	Table.set("Line angle", Table.size, theta_deg);
	Table.update;
}

macro "Two-line distance [f4]" {
	requires("1.30k");
	if (selectionType() == -1) {
		exit("[Two-lines distance]: Please select three points!");
	}
	
	getSelectionCoordinates(x, y);
	if (x.length != 3) {
		exit("[Two-lines distance]: Please select three points!");
	}
	
	a = y[0] - y[1];
	b = x[1] - x[0];
	c = (x[0]-x[1])*y[0] + (y[1]-y[0])*x[0];
	ab2 = a*a + b*b;
	xc = (b*(b*x[2] - a*y[2]) - a*c) / ab2;
	yc = (a*(-b*x[2] + a*y[2])-b*c) / ab2;
	
	//-- Get pixel data
	getPixelSize(unit, pw, ph, pd);
	d = abs( (x[1]-x[0])*(y[0]-y[2]) - (x[0]-x[2])*(y[1]-y[0]) ) / sqrt(ab2) * pw;
	
	makeLine(x[0],y[0],x[1],y[1]);
	Overlay.addSelection("red");

	makeSelection("polyline", newArray(xc, x[2]), newArray(yc, y[2]));
	setForegroundColor(0, 255, 255);
	run("Dotted Line", "line=1 dash=6,6");
	run("Select None");
	
	Table.set("Line Distance", Table.size, d);
	Table.update;
}

macro "Two-line angle option [f3]" {
	
	Dialog.create("Set Two-line angle measurement");
	Dialog.addCheckbox("Obtuse angle", obtusedAngles);
	Dialog.show();

	obtusedAngles = Dialog.getCheckbox();
}

Installation

• Copy this file to macros/toolsets
• Open ImageJ > More tool menu (>> Icon on the right)
• Select "Basic measurement"

Usage

Circumradius

• Use "Multipoint"
• Select three points for calculating circumradius
• Press [F1]

Angle between two lines

• Use "Multipoint"
• Select four points
• Press [F2]
• Optional: Press [F3] to change between acute and obtuse angle measurement

Distance between a line and a point

• Use "Multipoint"
• Select three points (the first two points will be a line)
• Press [F4]