diff --git a/CMakeLists.txt b/CMakeLists.txt
index 2519a8f..15f04ee 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -174,6 +174,10 @@ set(SOURCES_CG
   src/image/image_get_pixel.c
   src/image/image_hflip.c
   src/image/image_hflip_alloc.c
+  src/image/image_rotate.c
+  src/image/image_rotate_around.c
+  src/image/image_rotate_around_scale.c
+  src/image/image_scale.c
   src/image/image_set_palette.c
   src/image/image_set_pixel.c
   src/image/image_sub.c
diff --git a/include/gint/image.h b/include/gint/image.h
index e6aad53..e1f4e39 100644
--- a/include/gint/image.h
+++ b/include/gint/image.h
@@ -448,15 +448,101 @@ image_t *image_sub(image_t const *src, int x, int y, int w, int h,
 // while transforming, which is especially useful on the VRAM.
 //---
 
-/* image_hflip(): Flip horizontally (supports in-place) */
-void image_hflip(image_t const *src, image_t *dst);
+/* image_hflip(): Flip horizontally
+   Formats: RGB16, P8
+   Size requirement: destination at least as large as source (no clipping)
+   Supports in-place: Yes */
+void image_hflip(image_t const *src, image_t *dst, bool copy_alpha);
 image_t *image_hflip_alloc(image_t const *src);
 
-/* image_vflip(): Flip vertically (supports in-place) */
-void image_vflip(image_t const *src, image_t *dst);
+/* image_vflip(): Flip vertically
+   Formats: RGB16, P8
+   Size requirement: destination at least as large as source (no clipping)
+   Supports in-place: Yes */
+void image_vflip(image_t const *src, image_t *dst, bool copy_alpha);
 image_t *image_vflip_alloc(image_t const *src);
 
-/* TODO: Geometric transforms */
+/* image_linear(): Linear transformation
+
+   This function implements a generic linear transformation. This is a powerful
+   function that can perform any combination of rotation, mirroring and scaling
+   with nearest-neighbor sampling.
+
+   The [image_linear_opt] structure defines the settings for the transform.
+   Users familiar with linear algebra might want to use it directly, but they
+   are most conveniently generated with the rotation and scaling functions
+   listed below.
+
+   Formats: RGB16, P8
+   Size requirement: none (clipping through image_linear_opt settings)
+   Supports in-place: No */
+
+struct image_linear_map {
+    /* The following parameters define the linear transformation as a mapping
+       from coordinates in the destination image (x and y) into coordinates in
+       the source image (u and v).
+       - (u, v) indicate where the top-left corner of the destination lands in
+         the source image.
+       - (dx_u, dx_v) indicate the source-image movement for each movement of
+         x += 1 in the destination.
+       - (dy_u, dy_v) indicate the source-image movement for each movement of
+         y += 1 in the destination.
+       All of these values are specified as 16:16 fixed-point, ie. they encode
+       decimal values by multiplying them by 65536. */
+    int u, v, dx_u, dx_v, dy_u, dy_v;
+
+    /* Dimensions of the source and destination */
+    int src_w, src_h, dst_w, dst_h;
+};
+
+void image_linear(image_t const *src, image_t *dst,
+    struct image_linear_map const *map);
+image_t *image_linear_alloc(image_t const *src,
+    struct image_linear_map const *map);
+
+/* image_scale(): Upscale or downscale an image
+
+   This function generates a linear map to be used in image_linear() to scale
+   the input image. The scaling factor gamma can be specified independently for
+   the x and y dimensions. It is expressed as 16:16 fixed-point; you can set
+   any decimal value multiplied by 65536, for instance 1.5*65536 to increase
+   the width and height by 50%. */
+void image_scale(image_t const *src, int gamma_x, int gamma_y,
+    struct image_linear_map *map);
+
+/* image_rotate(): Rotate an image around its center
+
+   This function generates a linear map to be used in image_linear() to perform
+   a rotation around the center of an image. If [resize=true], the target is
+   enlarged to make sure all the rotated pixels can be represented. This can
+   increase the final surface by a factor of up to 2. If the original image
+   doesn't extend to its corners, it is recommended to leave [resize=false] as
+   it noticeably affects performance. */
+void image_rotate(image_t const *src, float angle, bool resize,
+    struct image_linear_map *map);
+
+/* image_rotate_around(): Rotate an image around any point
+
+   This function generalizes image_rotate() by allowing rotations around any
+   center, even a point not within the image. The center is specified through
+   two coordinates (*center_x, *center_y). If the center is near the side of
+   the image, a normal rotation would move most of the pixels out of frame;
+   this function moves the frame to make sure the whole image remains visible.
+   *center_x and *center_y are updated to indicate the position of the center
+   of rotation within the new frame (the target image). */
+void image_rotate_around(image_t const *src, float angle, bool resize,
+    int *center_x, int *center_y, struct image_linear_map *map);
+
+/* image_rotate_around_scale(): Rotate an image around any point and scale it
+
+   This function generalizes image_rotate_around() by adding a scaling factor
+   to the transformation. The scaling factor gamma is expressed as 16:16
+   fixed-point. If [resize=true] the image is further extended to make sure no
+   parts are cut out, as in other rotation functions. */
+void image_rotate_around_scale(
+    image_t const *src, float angle, int gamma,
+    bool resize, int *center_x, int *center_y,
+    struct image_linear_map *map);
 
 //---
 // Color transforms
@@ -733,6 +819,10 @@ bool image_target(image_t const *src, image_t *dst, ...);
 #define image_target_arg6(c, ...) \
     IMAGE_TARGET_ ## c __VA_OPT__(, image_target_too_many_args(__VA_ARGS__))
 
+/* image_alpha_2(): Conditional alpha */
+#define image_alpha_2(fmt, copy_alpha) \
+        ((copy_alpha) ? 0x10000 : image_alpha(fmt))
+
 #endif /* FXCG50 */
 
 #ifdef __cplusplus
diff --git a/src/image/fixed.h b/src/image/fixed.h
new file mode 100644
index 0000000..b4c4474
--- /dev/null
+++ b/src/image/fixed.h
@@ -0,0 +1,29 @@
+//---
+// gint:image:fixed - Minimal fixed-point interface for linear transformations
+//---
+
+#ifndef GINT_IMAGE_FIXED
+#define GINT_IMAGE_FIXED
+
+/* Constants */
+#define fconst(x) ((x) * 65536)
+
+/* Multiplication */
+static inline int fmul(int x, int y)
+{
+    return ((int64_t)x * (int64_t)y) >> 32;
+}
+
+/* Multiplication with a scalar */
+static inline int fmuls(int x, int s)
+{
+    return ((int64_t)x * (int64_t)s) >> 16;
+}
+
+/* Division */
+static inline int fdiv(int x, int y)
+{
+    return ((int64_t)x << 16) / y;
+}
+
+#endif /* GINT_IMAGE_FIXED */
diff --git a/src/image/image_copy.c b/src/image/image_copy.c
index eef220f..ca7b700 100644
--- a/src/image/image_copy.c
+++ b/src/image/image_copy.c
@@ -16,8 +16,8 @@ void image_copy(image_t const *src, image_t *dst, bool copy_alpha)
 
     void *src_px = src->data;
     void *dst_px = dst->data;
-    int src_alpha = copy_alpha ? 0x10000 : image_alpha(src->format);
-    int dst_alpha = copy_alpha ? 0x10000 : image_alpha(dst->format);
+    int src_alpha = image_alpha_2(src->format, copy_alpha);
+    int dst_alpha = image_alpha_2(dst->format, copy_alpha);
 
     if(IMAGE_IS_RGB16(src->format) && IMAGE_IS_RGB16(dst->format)) {
         do {
diff --git a/src/image/image_hflip.c b/src/image/image_hflip.c
index 4a540c1..b4f97dc 100644
--- a/src/image/image_hflip.c
+++ b/src/image/image_hflip.c
@@ -1,14 +1,14 @@
 #include <gint/image.h>
 
-void image_hflip(image_t const *src, image_t *dst)
+void image_hflip(image_t const *src, image_t *dst, bool copy_alpha)
 {
     if(!image_target(src, dst, DATA_RW, SAME_DEPTH, SAME_SIZE))
         return;
 
     void *src_px = src->data;
     void *dst_px = dst->data;
-    int src_alpha = image_alpha(src->format);
-    int dst_alpha = image_alpha(dst->format);
+    int src_alpha = image_alpha_2(src->format, copy_alpha);
+    int dst_alpha = image_alpha_2(dst->format, copy_alpha);
     int h = src->height;
 
     if(IMAGE_IS_RGB16(src->format)) {
diff --git a/src/image/image_hflip_alloc.c b/src/image/image_hflip_alloc.c
index 6d9f0fc..cfe1e9f 100644
--- a/src/image/image_hflip_alloc.c
+++ b/src/image/image_hflip_alloc.c
@@ -11,7 +11,6 @@ image_t *image_hflip_alloc(image_t const *src)
         return NULL;
     }
 
-    image_clear(dst);
-    image_hflip(src, dst);
+    image_hflip(src, dst, true);
     return dst;
 }
diff --git a/src/image/image_rotate.c b/src/image/image_rotate.c
new file mode 100644
index 0000000..3d72478
--- /dev/null
+++ b/src/image/image_rotate.c
@@ -0,0 +1,13 @@
+#include <gint/image.h>
+
+void image_rotate(image_t const *src, float angle, bool resize,
+    struct image_linear_map *map)
+{
+    if(!image_valid(src))
+        return;
+
+    int center_x = src->width / 2;
+    int center_y = src->height / 2;
+
+    image_rotate_around(src, angle, resize, &center_x, &center_y, map);
+}
diff --git a/src/image/image_rotate_around.c b/src/image/image_rotate_around.c
new file mode 100644
index 0000000..bf554e5
--- /dev/null
+++ b/src/image/image_rotate_around.c
@@ -0,0 +1,9 @@
+#include <gint/image.h>
+#include "fixed.h"
+
+void image_rotate_around(image_t const *src, float angle, bool resize,
+    int *center_x, int *center_y, struct image_linear_map *map)
+{
+    image_rotate_around_scale(src, angle, fconst(1.0), resize, center_x,
+        center_y, map);
+}
diff --git a/src/image/image_rotate_around_scale.c b/src/image/image_rotate_around_scale.c
new file mode 100644
index 0000000..65faf97
--- /dev/null
+++ b/src/image/image_rotate_around_scale.c
@@ -0,0 +1,16 @@
+#include <gint/image.h>
+#include "fixed.h"
+
+void image_rotate_around_scale(image_t const *src, float angle, int gamma,
+    bool resize, int *center_x, int *center_y, struct image_linear_map *map)
+{
+    if(!image_valid(src))
+        return;
+
+    map->src_w = src->width;
+    map->src_h = src->height;
+
+    /* Don't try to resize cleanly; just add a √2 factor in both dimensions if
+       [resize=true] to make sure everything fits */
+    ;
+}
diff --git a/src/image/image_scale.c b/src/image/image_scale.c
new file mode 100644
index 0000000..f038c57
--- /dev/null
+++ b/src/image/image_scale.c
@@ -0,0 +1,24 @@
+#include <gint/image.h>
+#include "fixed.h"
+
+void image_scale(image_t const *src, int gamma_x, int gamma_y,
+    struct image_linear_map *map)
+{
+    if(!image_valid(src))
+        return;
+
+    int inv_gamma_x = fdiv(fconst(1), gamma_x);
+    int inv_gamma_y = fdiv(fconst(1), gamma_y);
+
+    map->u = fconst(0);
+    map->v = fconst(0);
+    map->dx_u = inv_gamma_x;
+    map->dx_v = 0;
+    map->dy_u = 0;
+    map->dy_v = inv_gamma_y;
+
+    map->src_w = src->width;
+    map->src_h = src->height;
+    map->dst_w = fmuls(src->width, gamma_x);
+    map->dst_h = fmuls(src->height, gamma_y);
+}
diff --git a/src/image/image_vflip.c b/src/image/image_vflip.c
index 1c4f324..e56de77 100644
--- a/src/image/image_vflip.c
+++ b/src/image/image_vflip.c
@@ -21,7 +21,7 @@ static void copy_row_p8(int8_t *src, int8_t *dst, int src_alpha, int width)
     }
 }
 
-void image_vflip(image_t const *src, image_t *dst)
+void image_vflip(image_t const *src, image_t *dst, bool copy_alpha)
 {
     if(!image_target(src, dst, DATA_RW, SAME_DEPTH, SAME_SIZE))
         return;
@@ -32,8 +32,8 @@ void image_vflip(image_t const *src, image_t *dst)
     void *dst_top = dst->data;
     void *dst_bot = dst->data + (h - 1) * dst->stride;
 
-    int src_alpha = image_alpha(src->format);
-    int dst_alpha = image_alpha(dst->format);
+    int src_alpha = image_alpha_2(src->format, copy_alpha);
+    int dst_alpha = image_alpha_2(dst->format, copy_alpha);
 
     int row_length = src->stride;
     void *row = malloc(row_length);
diff --git a/src/image/image_vflip_alloc.c b/src/image/image_vflip_alloc.c
index ef26c91..21442e5 100644
--- a/src/image/image_vflip_alloc.c
+++ b/src/image/image_vflip_alloc.c
@@ -11,7 +11,6 @@ image_t *image_vflip_alloc(image_t const *src)
         return NULL;
     }
 
-    image_clear(dst);
-    image_vflip(src, dst);
+    image_vflip(src, dst, true);
     return dst;
 }