diff --git a/test/tutorial/tut03.cpp b/test/tutorial/tut03.cpp
index 9ad991ee..24b0ffa9 100644
--- a/test/tutorial/tut03.cpp
+++ b/test/tutorial/tut03.cpp
@@ -393,8 +393,8 @@ public:
                 ""
                 "float mylen(vec2 p) {"
                 //"    return abs(p.x) + abs(p.y);"
-                //"    return p.x * p.x + p.y * p.y;"
-                "    return length(p);"
+                "    return 0.001 + p.x * p.x + p.y * p.y;"
+                //"    return 0.001 + length(p);"
                 "}"
                 ""
                 /* Get the coordinate of the nearest point in slice 0 in xy,
@@ -407,10 +407,11 @@ public:
                 "    p += vec2(in_ZoomSettings[0][0], -in_ZoomSettings[0][1]);"
                 "    p += vec2(0.5, 0.5);"
                 "    vec2 q = p + 0.5 * in_TexelSize.xy;"
-                "    q -= mod(q, 2.0 * in_TexelSize.xy);"
-                "    q += 0.5 * in_TexelSize.xy;"
+                "    q = in_TexelSize.xy"
+                "         * (1.0 + 2.0 * floor(q * 0.5 * in_TexelSize.zw));"
+                "    vec2 r = q - 0.5 * in_TexelSize.xy;"
                 "    float l = (abs(q.x - 0.5) < 0.5 && abs(q.y - 0.5) < 0.5)"
-                "             ? 1.0 / mylen(q - p) : 0.0;"
+                "             ? 1.0 / mylen(r - p) : 0.0;"
                 "    return vec3(q * vec2(1.0, 0.25), l);"
                 "}"
                 ""
@@ -420,10 +421,11 @@ public:
                 "    p += vec2(in_ZoomSettings[1][0], -in_ZoomSettings[1][1]);"
                 "    p += vec2(0.5, 0.5);"
                 "    vec2 q = p + -0.5 * in_TexelSize.xy;"
-                "    q -= mod(q, 2.0 * in_TexelSize.xy);"
-                "    q += 1.5 * in_TexelSize.xy;"
+                "    q = in_TexelSize.xy"
+                "         * (1.0 + 2.0 * floor(q * 0.5 * in_TexelSize.zw));"
+                "    vec2 r = q - -0.5 * in_TexelSize.xy;"
                 "    float l = (abs(q.x - 0.5) < 0.5 && abs(q.y - 0.5) < 0.5)"
-                "             ? 1.0 / mylen(q - p) : 0.0;"
+                "             ? 1.0 / mylen(r - p) : 0.0;"
                 "    return vec3(q * vec2(1.0, 0.25) + vec2(0.0, 0.25), l);"
                 "}"
                 ""
@@ -433,10 +435,11 @@ public:
                 "    p += vec2(in_ZoomSettings[2][0], -in_ZoomSettings[2][1]);"
                 "    p += vec2(0.5, 0.5);"
                 "    vec2 q = p + vec2(0.5, -0.5) * in_TexelSize.xy;"
-                "    q -= mod(q, 2.0 * in_TexelSize.xy);"
-                "    q += vec2(0.5, 1.5) * in_TexelSize.xy;"
+                "    q = in_TexelSize.xy"
+                "         * (1.0 + 2.0 * floor(q * 0.5 * in_TexelSize.zw));"
+                "    vec2 r = q - vec2(0.5, -0.5) * in_TexelSize.xy;"
                 "    float l = (abs(q.x - 0.5) < 0.5 && abs(q.y - 0.5) < 0.5)"
-                "             ? 1.0 / mylen(q - p) : 0.0;"
+                "             ? 1.0 / mylen(r - p) : 0.0;"
                 "    return vec3(q * vec2(1.0, 0.25) + vec2(0.0, 0.50), l);"
                 "}"
                 ""
@@ -446,10 +449,11 @@ public:
                 "    p += vec2(in_ZoomSettings[3][0], -in_ZoomSettings[3][1]);"
                 "    p += vec2(0.5, 0.5);"
                 "    vec2 q = p + vec2(-0.5, 0.5) * in_TexelSize.xy;"
-                "    q -= mod(q, 2.0 * in_TexelSize.xy);"
-                "    q += vec2(1.5, 0.5) * in_TexelSize.xy;"
+                "    q = in_TexelSize.xy"
+                "         * (1.0 + 2.0 * floor(q * 0.5 * in_TexelSize.zw));"
+                "    vec2 r = q - vec2(-0.5, 0.5) * in_TexelSize.xy;"
                 "    float l = (abs(q.x - 0.5) < 0.5 && abs(q.y - 0.5) < 0.5)"
-                "             ? 1.0 / mylen(q - p) : 0.0;"
+                "             ? 1.0 / mylen(r - p) : 0.0;"
                 "    return vec3(q * vec2(1.0, 0.25) + vec2(0.0, 0.75), l);"
                 "}"
                 ""
@@ -459,10 +463,6 @@ public:
 #else
                 "    vec2 coord = gl_TexCoord[0].xy;"
 #endif
-                /* Slightly shift our pixel so that it does not lie at
-                 * an exact texel boundary. This would lead to visual
-                 * artifacts. */
-                "    coord -= 0.1 * in_TexelSize.xy;"
                 /* Get a pixel from each slice */
                 "    vec3 k0 = nearest0(coord);"
                 "    vec3 k1 = nearest1(coord);"