--- ray/src/common/fvect.c	1989/05/08 08:40:56	1.3
+++ 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;
@@ -83,6 +82,16 @@ register FVECT  vres, v1, v2;
 }
 
 
+fvsum(vres, v0, v1, f)		/* vres = v0 + f*v1 */
+FVECT  vres, v0, v1;
+double  f;
+{
+	vres[0] = v0[0] + f*v1[0];
+	vres[1] = v0[1] + f*v1[1];
+	vres[2] = v0[2] + f*v1[2];
+}
+
+
 double
 normalize(v)			/* normalize a vector, return old magnitude */
 register FVECT  v;
@@ -94,15 +103,36 @@ 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);
+}
+
+
+spinvector(vres, vorig, vnorm, theta)	/* rotate vector around normal */
+FVECT  vres, vorig, vnorm;
+double  theta;
+{
+	double  sint, cost, normprod;
+	FVECT  vperp;
+	register int  i;
+	
+	if (theta == 0.0) {
+		if (vres != vorig)
+			VCOPY(vres, vorig);
+		return;
+	}
+	cost = cos(theta);
+	sint = sin(theta);
+	normprod = DOT(vorig, vnorm)*(1.-cost);
+	fcross(vperp, vnorm, vorig);
+	for (i = 0; i < 3; i++)
+		vres[i] = vorig[i]*cost + vnorm[i]*normprod + vperp[i]*sint;
 }