diff --git a/src/xrint.h b/src/xrint.h
index 01756afab..f41058f60 100644
--- a/src/xrint.h
+++ b/src/xrint.h
@@ -564,6 +564,9 @@ XrTransformPointWithoutTranslate(XrTransform *transform, XPointDouble *pt);
 void
 XrTransformPoint(XrTransform *transform, XPointDouble *pt);
 
+void
+XrTransformEigenValues(XrTransform *transform, double *lambda1, double *lambda2);
+
 /* xrtraps.c */
 void
 XrTrapsInit(XrTraps *traps);
diff --git a/src/xrpen.c b/src/xrpen.c
index 266eec1a8..95f0f0f98 100644
--- a/src/xrpen.c
+++ b/src/xrpen.c
@@ -26,7 +26,7 @@
 #include "xrint.h"
 
 static int
-_XrPenVerticesNeeded(double radius, double tolerance);
+_XrPenVerticesNeeded(double radius, double tolerance, XrTransform *matrix);
 
 static void
 _XrPenComputeSlopes(XrPen *pen);
@@ -77,7 +77,7 @@ XrPenInit(XrPen *pen, double radius, XrGState *gstate)
     pen->radius = radius;
     pen->tolerance = gstate->tolerance;
 
-    pen->num_vertices = _XrPenVerticesNeeded(radius, gstate->tolerance);
+    pen->num_vertices = _XrPenVerticesNeeded(radius, gstate->tolerance, &gstate->ctm);
 
     pen->vertex = malloc(pen->num_vertices * sizeof(XrPenVertex));
     if (pen->vertex == NULL) {
@@ -199,17 +199,23 @@ XrPenAddPoints(XrPen *pen, XrPenTaggedPoint *pt, int num_pts)
 }
 
 static int
-_XrPenVerticesNeeded(double radius, double tolerance)
+_XrPenVerticesNeeded(double radius, double tolerance, XrTransform *matrix)
 {
-    /* XXX: BUG: This calculation needs to be corrected to account for
-       the fact that the radius is specified in user space, while the
-       tolerance is specified in device space. */
+    double e1, e2, emax, theta;
+
     if (tolerance > radius) {
 	return 4;
-    } else {
-	double theta = acos(1 - tolerance/radius);
-	return ceil(M_PI / theta);
-    }
+    } 
+
+    XrTransformEigenValues(matrix, &e1, &e2);
+
+    if (fabs(e1) > fabs(e2))
+	emax = fabs(e1);
+    else
+	emax = fabs(e2);
+
+    theta = acos(1 - tolerance/(emax * radius));
+    return ceil(M_PI / theta);
 }
 
 static void
diff --git a/src/xrtransform.c b/src/xrtransform.c
index 97cb083b8..7d41e9b3a 100644
--- a/src/xrtransform.c
+++ b/src/xrtransform.c
@@ -151,3 +151,35 @@ XrTransformPoint(XrTransform *transform, XPointDouble *pt)
     pt->x += transform->m[2][0];
     pt->y += transform->m[2][1];
 }
+
+void
+XrTransformEigenValues(XrTransform *transform, double *lambda1, double *lambda2)
+{
+    /* The eigenvalues of an NxN matrix M are found by solving the polynomial:
+
+       det(M - lI) = 0
+
+       which for our 2x2 matrix:
+
+       M = a b 
+           c d
+
+       gives:
+
+       l^2 - (a+d)l + (ad - bc) = 0
+
+       l = (a+d +/- sqrt(a^2 + 2ad + d^2 - 4(ad-bc))) / 2;
+    */
+
+    double a, b, c, d, rad;
+
+    a = transform->m[0][0];
+    b = transform->m[0][1];
+    c = transform->m[1][0];
+    d = transform->m[1][1];
+
+    rad = sqrt(a*a + 2*a*d + d*d - 4*(a*d - b*c));
+    *lambda1 = (a + d + rad) / 2.0;
+    *lambda2 = (a + d - rad) / 2.0;
+}
+
diff --git a/xrint.h b/xrint.h
index 01756afab..f41058f60 100644
--- a/xrint.h
+++ b/xrint.h
@@ -564,6 +564,9 @@ XrTransformPointWithoutTranslate(XrTransform *transform, XPointDouble *pt);
 void
 XrTransformPoint(XrTransform *transform, XPointDouble *pt);
 
+void
+XrTransformEigenValues(XrTransform *transform, double *lambda1, double *lambda2);
+
 /* xrtraps.c */
 void
 XrTrapsInit(XrTraps *traps);
diff --git a/xrpen.c b/xrpen.c
index 266eec1a8..95f0f0f98 100644
--- a/xrpen.c
+++ b/xrpen.c
@@ -26,7 +26,7 @@
 #include "xrint.h"
 
 static int
-_XrPenVerticesNeeded(double radius, double tolerance);
+_XrPenVerticesNeeded(double radius, double tolerance, XrTransform *matrix);
 
 static void
 _XrPenComputeSlopes(XrPen *pen);
@@ -77,7 +77,7 @@ XrPenInit(XrPen *pen, double radius, XrGState *gstate)
     pen->radius = radius;
     pen->tolerance = gstate->tolerance;
 
-    pen->num_vertices = _XrPenVerticesNeeded(radius, gstate->tolerance);
+    pen->num_vertices = _XrPenVerticesNeeded(radius, gstate->tolerance, &gstate->ctm);
 
     pen->vertex = malloc(pen->num_vertices * sizeof(XrPenVertex));
     if (pen->vertex == NULL) {
@@ -199,17 +199,23 @@ XrPenAddPoints(XrPen *pen, XrPenTaggedPoint *pt, int num_pts)
 }
 
 static int
-_XrPenVerticesNeeded(double radius, double tolerance)
+_XrPenVerticesNeeded(double radius, double tolerance, XrTransform *matrix)
 {
-    /* XXX: BUG: This calculation needs to be corrected to account for
-       the fact that the radius is specified in user space, while the
-       tolerance is specified in device space. */
+    double e1, e2, emax, theta;
+
     if (tolerance > radius) {
 	return 4;
-    } else {
-	double theta = acos(1 - tolerance/radius);
-	return ceil(M_PI / theta);
-    }
+    } 
+
+    XrTransformEigenValues(matrix, &e1, &e2);
+
+    if (fabs(e1) > fabs(e2))
+	emax = fabs(e1);
+    else
+	emax = fabs(e2);
+
+    theta = acos(1 - tolerance/(emax * radius));
+    return ceil(M_PI / theta);
 }
 
 static void
diff --git a/xrtransform.c b/xrtransform.c
index 97cb083b8..7d41e9b3a 100644
--- a/xrtransform.c
+++ b/xrtransform.c
@@ -151,3 +151,35 @@ XrTransformPoint(XrTransform *transform, XPointDouble *pt)
     pt->x += transform->m[2][0];
     pt->y += transform->m[2][1];
 }
+
+void
+XrTransformEigenValues(XrTransform *transform, double *lambda1, double *lambda2)
+{
+    /* The eigenvalues of an NxN matrix M are found by solving the polynomial:
+
+       det(M - lI) = 0
+
+       which for our 2x2 matrix:
+
+       M = a b 
+           c d
+
+       gives:
+
+       l^2 - (a+d)l + (ad - bc) = 0
+
+       l = (a+d +/- sqrt(a^2 + 2ad + d^2 - 4(ad-bc))) / 2;
+    */
+
+    double a, b, c, d, rad;
+
+    a = transform->m[0][0];
+    b = transform->m[0][1];
+    c = transform->m[1][0];
+    d = transform->m[1][1];
+
+    rad = sqrt(a*a + 2*a*d + d*d - 4*(a*d - b*c));
+    *lambda1 = (a + d + rad) / 2.0;
+    *lambda2 = (a + d - rad) / 2.0;
+}
+