--- ray/src/common/fvect.c	1991/03/19 13:14:19	1.5
+++ ray/src/common/fvect.c	1993/12/10 09:53:30	2.3
@@ -10,11 +10,10 @@ static char SCCSid[] = "$SunId$ LBL";
  *     8/14/85
  */
 
+#include  <math.h>
 #include  "fvect.h"
 
-#define  FTINY		1e-7
 
-
 double
 fdot(v1, v2)			/* return the dot product of two vectors */
 register FVECT  v1, v2;
@@ -104,16 +103,15 @@ register FVECT  v;
 	if (len <= 0.0)
 		return(0.0);
 	
-	/****** problematic
-	if (len >= (1.0-FTINY)*(1.0-FTINY) &&
-			len <= (1.0+FTINY)*(1.0+FTINY))
-		return(1.0);
-	******/
+	if (len <= 1.0+FTINY && len >= 1.0-FTINY)
+		len = 0.5 + 0.5*len;	/* first order approximation */
+	else
+		len = sqrt(len);
 
-	len = sqrt(len);
 	v[0] /= len;
 	v[1] /= len;
 	v[2] /= len;
+
 	return(len);
 }
 
@@ -122,20 +120,19 @@ spinvector(vres, vorig, vnorm, theta)	/* rotate vector
 FVECT  vres, vorig, vnorm;
 double  theta;
 {
-	extern double  sin(), cos();
-	double  sint, cost, dotp;
+	double  sint, cost, normprod;
 	FVECT  vperp;
 	register int  i;
 	
 	if (theta == 0.0) {
-		VCOPY(vres, vorig);
+		if (vres != vorig)
+			VCOPY(vres, vorig);
 		return;
 	}
-	sint = sin(theta);
 	cost = cos(theta);
-	dotp = DOT(vorig, vnorm);
+	sint = sin(theta);
+	normprod = DOT(vorig, vnorm)*(1.-cost);
 	fcross(vperp, vnorm, vorig);
 	for (i = 0; i < 3; i++)
-		vres[i] = vnorm[i]*dotp*(1.-cost) +
-				vorig[i]*cost + vperp[i]*sint;
+		vres[i] = vorig[i]*cost + vnorm[i]*normprod + vperp[i]*sint;
 }