Hologram: fix projection matrix

Fix projection matrix for Vulkan clip space instead of patching things up
in VS.

demos/Hologram/Hologram.cpp

@@ -585,12 +585,20 @@ void Hologram::prepare_framebuffers(VkSwapchainKHR swapchain)
 
 void Hologram::update_projection()
 {
-    float aspect = static_cast<float>(extent_.width) / static_cast<float>(extent_.height);
     const glm::vec3 center(0.0f);
     const glm::vec3 up(0.f, 0.0f, 1.0f);
     const glm::mat4 view = glm::lookAt(eye_pos_, center, up);
+
+    float aspect = static_cast<float>(extent_.width) / static_cast<float>(extent_.height);
     const glm::mat4 projection = glm::perspective(0.4f, aspect, 0.1f, 100.0f);
-    view_projection_ = projection * view;
+
+    // Vulkan clip space has inverted Y and half Z.
+    const glm::mat4 clip(1.0f,  0.0f, 0.0f, 0.0f,
+                         0.0f, -1.0f, 0.0f, 0.0f,
+                         0.0f,  0.0f, 0.5f, 0.0f,
+                         0.0f,  0.0f, 0.5f, 1.0f);
+
+    view_projection_ = clip * projection * view;
 }
 
 void Hologram::step_object(Object &obj, float obj_time, FrameData &data) const

demos/Hologram/Hologram.push_constant.vert

@@ -13,9 +13,6 @@ void main()
 {
 	vec4 pos = matrices.mvp * vec4(in_pos, 1.0);
 
-	pos.y = -pos.y;
-	pos.z = (pos.z + pos.w) / 2.0;
-
 	gl_Position = pos;
 	color = in_color;
 }

demos/Hologram/Hologram.vert

@@ -13,9 +13,6 @@ void main()
 {
 	vec4 pos = matrices.mvp * vec4(in_pos, 1.0);
 
-	pos.y = -pos.y;
-	pos.z = (pos.z + pos.w) / 2.0;
-
 	gl_Position = pos;
 	color = in_color;
 }