fix and improve: VAE tiling

- properly handle the upper left corner interpolating both x and y
- refactor out lerp
- use smootherstep to preserve more detail and spend less area blending

ggml_extend.hpp

@@ -353,6 +353,16 @@ __STATIC_INLINE__ void ggml_split_tensor_2d(struct ggml_tensor* input,
     }
 }
 
+__STATIC_INLINE__ float ggml_lerp_f32(const float a, const float b, const float x) {
+    return (1 - x) * a + x * b;
+}
+
+// unclamped -> expects x in the range [0-1]
+__STATIC_INLINE__ float ggml_smootherstep_f32(const float x) {
+    GGML_ASSERT(x >= 0.f && x <= 1.f);
+    return x * x * x * (x * (6.0f * x - 15.0f) + 10.0f);
+}
+
 __STATIC_INLINE__ void ggml_merge_tensor_2d(struct ggml_tensor* input,
                                             struct ggml_tensor* output,
                                             int x,
@@ -368,12 +378,33 @@ __STATIC_INLINE__ void ggml_merge_tensor_2d(struct ggml_tensor* input,
                 float new_value = ggml_tensor_get_f32(input, ix, iy, k);
                 if (overlap > 0) {  // blend colors in overlapped area
                     float old_value = ggml_tensor_get_f32(output, x + ix, y + iy, k);
-                    if (x > 0 && ix < overlap) {  // in overlapped horizontal
-                        ggml_tensor_set_f32(output, old_value + (new_value - old_value) * (ix / (1.0f * overlap)), x + ix, y + iy, k);
+                    const bool inside_x_overlap = x > 0 && ix < overlap;
+                    const bool inside_y_overlap = y > 0 && iy < overlap;
+                    if (inside_x_overlap && inside_y_overlap) {
+                        // upper left corner needs to be interpolated in both directions
+                        const float x_f = ix / float(overlap);
+                        const float y_f = iy / float(overlap);
+                        // TODO: try `x+y - 1`
+                        const float f = std::min(x_f, y_f); // min of both
+                        ggml_tensor_set_f32(
+                            output,
+                            ggml_lerp_f32(old_value, new_value, ggml_smootherstep_f32(f)),
+                            x + ix, y + iy, k
+                        );
                         continue;
-                    }
-                    if (y > 0 && iy < overlap) {  // in overlapped vertical
-                        ggml_tensor_set_f32(output, old_value + (new_value - old_value) * (iy / (1.0f * overlap)), x + ix, y + iy, k);
+                    } else if (inside_x_overlap) {
+                        ggml_tensor_set_f32(
+                            output,
+                            ggml_lerp_f32(old_value, new_value, ggml_smootherstep_f32(ix / float(overlap))),
+                            x + ix, y + iy, k
+                        );
+                        continue;
+                    } else if (inside_y_overlap) {
+                        ggml_tensor_set_f32(
+                            output,
+                            ggml_lerp_f32(old_value, new_value, ggml_smootherstep_f32(iy / float(overlap))),
+                            x + ix, y + iy, k
+                        );
                         continue;
                     }
                 }