UPBGE: Fix GLSL inverse support.

The inverse GLSL function is needed for geometry instancing, but this
function is quite recent as it is unsupported before GLSL 1.40.

To avoid forbid geometry instancing for a GLSL function support, an
equivalent of the inverse function is written. This equivalent is put
in gpu_shader_lib.glsl in the marco test : __VERSION__ < 140.

This file is added in both vertex and fragment shader when compiling it.

source/blender/gpu/CMakeLists.txt

@@ -128,6 +128,7 @@ data_to_c_simple(shaders/gpu_shader_fx_dof_hq_vert.glsl SRC)
 data_to_c_simple(shaders/gpu_shader_fx_dof_hq_geo.glsl SRC)
 data_to_c_simple(shaders/gpu_shader_fx_depth_resolve.glsl SRC)
 data_to_c_simple(shaders/gpu_shader_fx_lib.glsl SRC)
+data_to_c_simple(shaders/gpu_shader_lib.glsl SRC)
 
 if(WITH_GAMEENGINE)
 	add_definitions(-DWITH_GAMEENGINE)

source/blender/gpu/intern/gpu_shader.c

@@ -66,6 +66,7 @@ extern char datatoc_gpu_shader_fx_dof_hq_vert_glsl[];
 extern char datatoc_gpu_shader_fx_dof_hq_geo_glsl[];
 extern char datatoc_gpu_shader_fx_depth_resolve_glsl[];
 extern char datatoc_gpu_shader_fx_lib_glsl[];
+extern char datatoc_gpu_shader_lib_glsl[];
 
 static struct GPUShadersGlobal {
 	struct {
@@ -333,13 +334,14 @@ GPUShader *GPU_shader_create_ex(const char *vertexcode,
 	gpu_shader_standard_extensions(standard_extensions, geocode != NULL);
 
 	if (vertexcode) {
-		const char *source[6];
+		const char *source[7];
 		/* custom limit, may be too small, beware */
 		int num_source = 0;
 
 		source[num_source++] = gpu_shader_version();
 		source[num_source++] = standard_extensions;
 		source[num_source++] = standard_defines;
+		source[num_source++] = datatoc_gpu_shader_lib_glsl;
 
 		if (defines) source[num_source++] = defines;
 		if (resetline) {
@@ -364,12 +366,13 @@ GPUShader *GPU_shader_create_ex(const char *vertexcode,
 	}
 
 	if (fragcode) {
-		const char *source[8];
+		const char *source[9];
 		int num_source = 0;
 
 		source[num_source++] = gpu_shader_version();
 		source[num_source++] = standard_extensions;
 		source[num_source++] = standard_defines;
+		source[num_source++] = datatoc_gpu_shader_lib_glsl;
 
 #ifdef WITH_OPENSUBDIV
 		/* TODO(sergey): Move to fragment shader source code generation. */
@@ -407,12 +410,13 @@ GPUShader *GPU_shader_create_ex(const char *vertexcode,
 	}
 
 	if (geocode) {
-		const char *source[7];
+		const char *source[8];
 		int num_source = 0;
 
 		source[num_source++] = gpu_shader_version();
 		source[num_source++] = standard_extensions;
 		source[num_source++] = standard_defines;
+		source[num_source++] = datatoc_gpu_shader_lib_glsl;
 
 		if (defines) source[num_source++] = defines;
 		if (resetline) {

source/blender/gpu/shaders/gpu_shader_lib.glsl

@@ -0,0 +1,45 @@
+#if __VERSION__ < 140
+/* Manual implementation of inverse(mat4) for GLSL version before 1.40, 
+ * copied from https://github.com/stackgl/glsl-inverse/blob/master/index.glsl
+ */
+
+mat4 inverse(mat4 m) {
+	float a00 = m[0][0], a01 = m[0][1], a02 = m[0][2], a03 = m[0][3],
+	a10 = m[1][0], a11 = m[1][1], a12 = m[1][2], a13 = m[1][3],
+	a20 = m[2][0], a21 = m[2][1], a22 = m[2][2], a23 = m[2][3],
+	a30 = m[3][0], a31 = m[3][1], a32 = m[3][2], a33 = m[3][3],
+
+	b00 = a00 * a11 - a01 * a10,
+	b01 = a00 * a12 - a02 * a10,
+	b02 = a00 * a13 - a03 * a10,
+	b03 = a01 * a12 - a02 * a11,
+	b04 = a01 * a13 - a03 * a11,
+	b05 = a02 * a13 - a03 * a12,
+	b06 = a20 * a31 - a21 * a30,
+	b07 = a20 * a32 - a22 * a30,
+	b08 = a20 * a33 - a23 * a30,
+	b09 = a21 * a32 - a22 * a31,
+	b10 = a21 * a33 - a23 * a31,
+	b11 = a22 * a33 - a23 * a32,
+
+	det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
+
+	return mat4(
+		a11 * b11 - a12 * b10 + a13 * b09,
+		a02 * b10 - a01 * b11 - a03 * b09,
+		a31 * b05 - a32 * b04 + a33 * b03,
+		a22 * b04 - a21 * b05 - a23 * b03,
+		a12 * b08 - a10 * b11 - a13 * b07,
+		a00 * b11 - a02 * b08 + a03 * b07,
+		a32 * b02 - a30 * b05 - a33 * b01,
+		a20 * b05 - a22 * b02 + a23 * b01,
+		a10 * b10 - a11 * b08 + a13 * b06,
+		a01 * b08 - a00 * b10 - a03 * b06,
+		a30 * b04 - a31 * b02 + a33 * b00,
+		a21 * b02 - a20 * b04 - a23 * b00,
+		a11 * b07 - a10 * b09 - a12 * b06,
+		a00 * b09 - a01 * b07 + a02 * b06,
+		a31 * b01 - a30 * b03 - a32 * b00,
+		a20 * b03 - a21 * b01 + a22 * b00) / det;
+}
+#endif

source/blender/gpu/shaders/gpu_shader_vertex.glsl

@@ -108,9 +108,10 @@ void main()
 						vec4(ininstmatrix[1], ininstposition.y),
 						vec4(ininstmatrix[2], ininstposition.z),
 						vec4(0.0, 0.0, 0.0, 1.0));
+
 	varinstmat = transpose(instmat);
-	varinstinvmat = inverse(varinstmat);
 	varinstlocaltoviewmat = unfviewmat * varinstmat;
+	varinstinvmat = inverse(varinstmat);
 	varinstinvlocaltoviewmat = inverse(varinstlocaltoviewmat);
 	varinstcolor = ininstcolor;