compute initial log quaternion

lnQuat.js

// theta - angle in radians, d = {x, y, z } direction/unnormalized
function lnQuat( theta, d ){
			// if no rotation, then nothing.
			const dl = 1/Math.sqrt( d.x*d.x + d.y*d.y + d.z*d.z ); // 1/ d length = normalize d

			const t  = theta/2;
			const ct2 = Math.cos( t );  // sqrt( 1/2(1 + cos theta))  - half angle subst
			const st2 = Math.sin( t );  // sqrt( 1/2(1 - cos theta))  - half angle subst
			const w = ct2;
			const x = dl * d.x * st2;
			const y = dl * d.y * st2;
			const z = dl * d.z * st2;
	
			// sqrt( 1/2(1 + cos theta)) * sqrt( 1/2(1 + cos theta))  
	               //     + sqrt( 1/2(1 - cos theta) )*sqrt( 1/2(1 - cos theta)) * x*x
			//    + sqrt( 1/2(1 - cos theta) )*sqrt( 1/2(1 - cos theta)) * y*y
			//    + sqrt( 1/2(1 - cos theta) )*sqrt( 1/2(1 - cos theta)) * z*z )
	
		// for R below, substitute terms... (also factor x,y,z from sin value)
			// sqrt( 1/2(1 + cos theta)) * sqrt( 1/2(1 + cos theta)) 
			//     + sqrt( 1/2(1 - cos theta))*sqrt( 1/2(1 - cos theta)) 
			//           * ( x*x+y*y+z*z )

		// collapse sqrt(n)*sqrt(n) to n
			// 1/2(1 + cos theta)  + 1/2(1 - cos theta) * ( x*x+y*y+z*z )
	
	        // the length of the direction part is normalized and is always 1
			// 1/2(1 + cos theta)  + 1/2(1 - cos theta) * (1)
	
			// 1/2 ( 1 + cos theta + 1 - cos theta)
	
		// so this should always be 1??
			// 1
			const r  = w*w + x*x+y*y+z*z ;
	
}