Metal: nothing is rendered when using orthographic projection matrix - ios

Question

I am using the following code to create orthographic matrix:
Matrix4D Matrix4D::fromOrtho(double left, double right, double bottom, double top, double nearZ, double farZ)
{
double ral = right + left;
double rsl = right - left;
double tab = top + bottom;
double tsb = top - bottom;
double fan = farZ + nearZ;
double fsn = farZ - nearZ;
return Matrix4D ( 2.0f / rsl, 0.0f, 0.0f, 0.0f,
0.0f, 2.0f / tsb, 0.0f, 0.0f,
0.0f, 0.0f, -2.0f / fsn, 0.0f,
-ral / rsl, -tab / tsb, -fan / fsn, 1.0f);
}
and use the following parameters:
double widthToHeightRatio = screenWidth / screenHeight;
Matrix4D::fromOrtho(-10, 10, -7, 7 ,0.1, 5000);
The left, right, bottom and top parameters are actually calculates as a function of the camera eye and center coordinates, but this is an example for result parameters.
The same matrix works well with OpenGL but not working with Metal. When the matrix is a perspective matrix, everything works well also in Metal.
What might be the problem?

Answer 1

Both perspective and ortho projection matrices from GL are invalid in Metal, because the z range is different. Some matrices MAY still work because your z-clip range is overly-deep in OpenGL so it happens to be deep enough to let fragments through in Metal as well, but this is a bad thing to bank on.
From the Metal Programming Guide, p. 51 “Working with Viewport and Pixel Space Coordinates”:
Metal defines its Normalized Device Coordinate (NDC) system as a
2x2x1 cube with its center at (0, 0, 0.5). The left and bottom for x
and y, respectively, of the NDC system are specified as -1. The right
and top for x and y, respectively, of the NDC system are specified as
+1.
This is different from OpenGL, which has its z go from -1 to 1, in a 2x2x2 cube.
See this blog post for more details: http://blog.athenstean.com/post/135771439196/from-opengl-to-metal-the-projection-matrix
Update — User da1 found an alternate blog post, the above is currently down: http://metashapes.com/blog/opengl-metal-projection-matrix-problem

Answer 2

from AAPLTransfomations.mm this works for me (metal sample project)
simd::float4x4 AAPL::ortho2d(const float& left,
const float& right,
const float& bottom,
const float& top,
const float& near,
const float& far)
{
float sLength = 1.0f / (right - left);
float sHeight = 1.0f / (top - bottom);
float sDepth = 1.0f / (far - near);
simd::float4 P;
simd::float4 Q;
simd::float4 R;
simd::float4 S;
P.x = 2.0f * sLength;
P.y = 0.0f;
P.z = 0.0f;
P.w = 0.0f;
Q.x = 0.0f;
Q.y = 2.0f * sHeight;
Q.z = 0.0f;
Q.w = 0.0f;
R.x = 0.0f;
R.y = 0.0f;
R.z = sDepth;
R.w = 0.0f;
S.x = 0.0f;
S.y = 0.0f;
S.z = -near * sDepth;
S.w = 1.0f;
return simd::float4x4(P, Q, R, S);
} // ortho2d
and implemented by passing to your shader in the
constant_buffer[i].modelview_ortho_matrix = ortho2d(-2.0f, 2.0f, -2.0f, 2.0f, 0, 2); //_projectionMatrix * modelViewMatrix;
and then perhaps in your vertex shader
float4 in_position = float4(float3(vertex_array[vid].position), 1.0);
out.position = constants.modelview_ortho_matrix * in_position;