Name

    ARB_clip_control

Name Strings

    GL_ARB_clip_control

Contact

    Mark J. Kilgard, NVIDIA Corporation (mjk 'at' nvidia.com)

Contributors

    Timo Suoranta, Broadcom
    Piers Daniell, NVIDIA
    Stefan Dösinger, CodeWeavers
    Jeff Bolz, NVIDIA
    John McDonald, NVIDIA
    Brian Paul, VMware, Mesa3D
    Jason Mitchell, Valve
    Alex Corscadden, VMware
    Simon Bennett, VMware
    Mark Callow, HI Corporation
    Patrick Doane, Blizzard
    Pat Brown, NVIDIA
    Brano Kemen

Notice

    Copyright (c) 2014 The Khronos Group Inc. Copyright terms at
        http://www.khronos.org/registry/speccopyright.html

Status

    Complete.
    Approved by the ARB on June 26, 2014.
    Ratified by the Khronos Board of Promoters on August 7, 2014.

Version

    Last Modified Date:  2015/09/17
    NVIDIA Revision:     18

Number

    ARB Extension #160

Dependencies

    Written based on the wording of the OpenGL 4.4 (Compatibility Profile)
    specification.

Overview

    This extension provides additional clip control modes to configure how
    clip space is mapped to window space.  This extension's goal is to 1)
    allow OpenGL to effectively match Direct3D's coordinate system
    conventions, and 2) potentially improve the numerical precision of the Z
    coordinate mapping.

    Developers interested in this functionality may be porting content
    from Direct3D to OpenGL and/or interested in improving the numerical
    accuracy of depth testing, particularly with floating-point depth
    buffers.

    OpenGL's initial and conventional clip control state is configured by:

        glClipControl(GL_LOWER_LEFT, GL_NEGATIVE_ONE_TO_ONE);

    where geometry with (x,y) normalized device coordinates of (-1,-1)
    correspond to the lower-left corner of the viewport and the near and far
    planes correspond to z normalized device coordinates of -1 and +1,
    respectively.

    This extension can be used to render content used in a Direct3D
    application in OpenGL in a straightforward way without modifying vertex or
    matrix data.  When rendering into a window, the command

        glClipControl(GL_LOWER_LEFT, GL_ZERO_TO_ONE);

    configures the near clip plane to correspond to a z normalized device
    coordinate of 0 as in Direct3D.  Geometry with (x,y) normalized device
    coordinates of (-1,-1) correspond to the lower-left corner of the viewport
    in Direct3D, so no change relative to OpenGL conventions is needed there.
    Other state related to screen-space coordinates may need to be modified
    for the application to map from Direct3D to OpenGL window coordinate
    conventions.  For example, the viewport rectangle in Direct3D needs to be
    inverted within the window to work properly in OpenGL windowed rendering:

       glViewport(d3d_viewport_x,
                  window_height - (d3d_viewport_y + d3d_viewport_height),
                  d3d_viewport_width, d3d_viewport_height);

    When rendering Direct3D content into a framebuffer object in OpenGL, there
    is one complication -- how to get a correct image *out* of the related
    textures.  Direct3D applications would expect a texture coordinate of
    (0,0) to correspond to the upper-left corner of a rendered image, while
    OpenGL FBO conventions would map (0,0) to the lower-left corner of the
    rendered image.  For applications wishing to use Direct3D content with
    unmodified texture coordinates, the command

        glClipControl(GL_UPPER_LEFT, GL_ZERO_TO_ONE);

    configures the OpenGL to invert geometry vertically inside the viewport.
    Content at the top of the viewport for Direct3D will be rendered to the
    bottom of the viewport from the point of view of OpenGL, but will have a
    <t> texture coordinate of zero in both cases.  When operating in this
    mode, applications need not invert the programmed viewport rectangle as
    recommended for windowed rendering above.

    Applications happy with OpenGL's origin conventions but seeking
    potentially improved depth precision can configure clip controls using:

        glClipControl(GL_LOWER_LEFT, GL_ZERO_TO_ONE);

    to avoid the loss of precision from the DepthRange transformation
    (which by default is z_window = z_ndc * 0.5 + 0.5).

New Procedures and Functions

    void ClipControl(enum origin, enum depth);

New Tokens

    Accepted by the <origin> parameter of ClipControl:

        LOWER_LEFT                                  0x8CA1
        UPPER_LEFT                                  0x8CA2

    Accepted by the <depth> parameter of ClipControl:

        NEGATIVE_ONE_TO_ONE                         0x935E
        ZERO_TO_ONE                                 0x935F

    Accepted by the <pname> parameter of GetBooleanv, GetIntegerv,
    GetFloatv, and GetDoublev:

        CLIP_ORIGIN                                 0x935C
        CLIP_DEPTH_MODE                             0x935D

Additions to Chapter 13 of the OpenGL 4.4 (Compatibility Profile)
Specification (Fixed-Function Vertex Post-Processing)

 -- Modify section 13.5 "Primitive Clipping"

    Insert before the 1st paragraph...

    "The command

        ClipControl(enum origin, enum depth);

    controls the clipping volume behavior.  /origin/ must be either
    LOWER_LEFT or UPPER_LEFT, otherwise the error INVALID_ENUM is
    generated.  /depth/ must be either NEGATIVE_ONE_TO_ONE or
    ZERO_TO_ONE, otherwise the error INVALID_ENUM is generated.

      These parameters update the clip control origin and
    depth mode respectively.  The state required for clip control is one
    bit for clip control origin and one bit for clip control depth mode.
    The initial value of the clip control origin is LOWER_LEFT and the
    initial value of the depth mode is NEGATIVE_ONE_TO_ONE.

      The error INVALID_OPERATION is generated if ClipControl is
    executed between the execution of Begin and the corresponding
    execution of End."

    Replace the first paragraph with...

    "Primitives are clipped to the clip volume. In clip coordinates,
    the view volume is defined by

        -w_c <= x_c <= w_c
        -w_c <= y_c <= w_c
          zm <= z_c <= w_c

     where zm is -w_c when the clip control depth mode is
     NEGATIVE_ONE_TO_ONE or zero when the mode is ZERO_TO_ONE."

     Change the last sentence of the 7th paragraph to read...

     "If depth clamping is enabled, the

        zm <= z_c <= w_c

      plane equation (see the clip volume definition) is ignored by
      view volume clipping (effectively, there is no near or far plane
      clipping)."

 -- Modify section 13.6 "Coordinate Transformations"

    Replace the 3rd paragraph with (where ^T means transpose):

    "If a vertex in clip coordinates is given by (x_c y_c z_c w_c)^T
    then the vertex's normalized device coordinates are (x_d y_d z_d)^T =
    (x_c/w_c f*y_c/w_c z_c/w_c)^T where /f/ is +1 when the clip control
    origin is LOWER_LEFT and -1 when the origin is UPPER_LEFT."

 -- Modify section 13.6.1 "Controlling the Viewport"

    Replace the 2nd sentence of the 1st paragraph with (where ^T means
    transpose):

    "The vertex's window coordinates, (x_w y_w z_w)^T are given by:

        ( x_w )     ( p_x/2 x_d + o_x )
        ( y_w )  =  ( p_y/2 y_d + o_y )
        ( z_w )     (     s z_d + b   )

    where s is (f-n)/2 and b is (n+f)/2 when the clip control depth mode
    is NEGATIVE_ONE_TO_ONE; or s is (f-n) and b is n when the mode
    is ZERO_TO_ONE."

Additions to Chapter 14 of the OpenGL 4.4 (Compatibility Profile)
Specification (Fixed-Function Primitive Assembly and Rasterization)

 -- Modify section 14.6.1 "Basic Polygon Rasterization"

    Replace the 3rd sentence of the 1st paragraph with:

    "One way to compute this area is

               n-1
               ___
               \
      a = 1/2 f \  x^i_w * y^i(+)1_w - x^i(+)1_w * y^i_w
                /
               /__

    where f is +1 when the clip control origin is LOWER_LEFT and -1 when
    the origin is UPPER_LEFT, x^i_w and y^i_w are the x and y window
    coordinates of the ith vertex of the n-vertex polygon (vertices
    are numbered starting at zero for purposes of this computation),
    and i(+)1 is (i+1) mod n."

Additions to the AGL/GLX/WGL Specifications

    None

GLX Protocol

    A new GL rendering command is added. The following command is sent to the
    server as part of a glXRender request:

        ClipControl
            2           12              rendering command length
            2           1340            rendering command opcode
            4           ENUM            origin
            4           ENUM            depth

Errors

    The error INVALID_ENUM is generated by ClipControl if origin is not
    LOWER_LEFT or UPPER_LEFT.

    The error INVALID_ENUM is generated by ClipControl if depth is not
    NEGATIVE_ONE_TO_ONE or ZERO_TO_ONE.

    The error INVALID_OPERATION is generated if ClipControl is executed
    between the execution of Begin and the corresponding execution of
    End.

New State

    Get Value         Type  Get Command  Initial Value        Description      Sec   Attribute
    ----------------  ----  -----------  -------------------  ---------------  ----  ---------
    CLIP_ORIGIN       Z2    GetIntegerv  LOWER_LEFT           Clip origin      13.5  xform
    CLIP_DEPTH_MODE   Z2    GetIntegerv  NEGATIVE_ONE_TO_ONE  Clip depth mode  13.5  xform

New Implementation Dependent State

    None

Issues

    1)  What should this extension be called?

        RESOLVED:  ARB_clip_control

        We frame this extension in terms of how the fixed-function
        transformation from clip coordinates to window coordinates
        is specified.  The crucial modifications to OpenGL's existing
        behavior involve controlling how clip space is interpreted.

        An upper-left origin is really simply negating (flipping) the
        clip space Y coordinate.  Subsequently the sense of counter-clockwise
        and clockwise for face culling must be adjusted (flipped).

        A zero-to-one Z mode involves adjusting the clipping equation
        for the clip space Z coordinate.  Subsequently the depth range
        transform equation must be adjusted (scaled and biased).

        Hence clip control is a sensible name.

    2)  Should this functionality be exposed with glEnable/glDisable or
        with a new command.

        RESOLVED:  With a new command, glClipControl.

        We note that this extension does not actually enable or disable
        functionality, but rather modifies an existing transformation.

        We note that Direct3D is different in two ways: clip Y inversion
        and zero-to-one clip Z.

        We note the difficulty of a clear enable name.
        GL_NEGATIVE_ONE_TO_ONE and GL_ZERO_TO_ONE
        are very explicit about how the Z clip coordinate is treated by
        the clip equations.  Likewise, GL_LOWER_LEFT and GL_UPPER_LEFT
        are explicit (and match the token names and meaning for the
        point sprite functionality).

        We also note the possibility for other possible conventions.
        For example, an origin at the center of the window.  Hence an
        enumeration of clip modes is a better choice.  Likewise, a future
        Z mode could expose W-buffering.

    3)  Why does unextended OpenGL have symmetric clip equations?

        RESOLVED:  This is a legacy of implementation worthy of some
        explanation...

        Handling the X, Y, and Z directions the same way better
        facilitates vector operation for hardware efficiency.

        When transformations are done with 32-bit IEEE-754 floating-point
        values, after transformation to clip space for clipping, the
        Z values are typically converted to fixed-point for use by a
        conventional 24-bit fixed-point depth buffer.

        The process of scaling by 0.5 and adding 0.5 to a 32-bit
        floating-point number in the range [-1,+1] has the effect of
        appropriately rounding the value so it can be efficiently
        bit-shifted into a 24-bit fixed-point value in the [0,1]
        range suitable for depth buffering via linear fixed-point
        interpolation.

    4)  Should the face culling behavior be modified in GL_UPPER_LEFT
        clip origin mode?

        RESOLVED:  Yes.

        See how the modifications to section 14.6.1 "Basic Polygon
        Rasterization" negate the sign of the polygon area when the clip
        control origin is GL_UPPER_LEFT.

        Since culling behavior is specified as CW (clockwise) or CCW
        (counter-clockwise) different triangle faces would be culled
        when the clip origin is changed, which would be an unacceptable
        side effect.

    5)  Are the projective matrices generated by glFrustum and glOrtho
        appropriate when the clip Z mode is GL_ZERO_TO_ONE?

        RESOLVED:  No.

    6)  Should the behavior of glFrustum and glOrtho change?

        RESOLVED:  No.

        It's not worth encumbering these routines with adjustments,
        plus it is easy to make the proper adjustments...

        Taking advantage of how matrix changes concatenate...

        If your clip control origin is GL_UPPER_LEFT, prior to your
        glFrustum or glOrtho command by:

            glScalef(1,-1,1);

        If your clip control depth mode is GL_ZERO_TO_ONE, precede
        your glFrustum or glOrtho command by:

            glTranslatef(0,0,0.5);
            glScalef(1,1,0.5);

        For example, if your code to configure the projection matrix
        reads:

            glMatrixMode(GL_PROJECTION);
            glLoadIdentity();
            glFrustum(-0.5, 0.5, -0.5, 0.5, 1, 3);

        And you wanted to call:

            glClipControl(GL_UPPER_LEFT, GL_ZERO_TO_ONE);

        Then configure your projection matrix as

            glMatrixMode(GL_PROJECTION);
            glLoadIdentity();
            // adjust for GL_UPPER_LEFT
            glScalef(1,-1,1);
            // adjust for GL_ZERO_TO_ONE
            glTranslatef(0,0,0.5);
            glScalef(1,1,0.5);
            glFrustum(-0.5, 0.5, -0.5, 0.5, 1, 3);

        Technically, the two glScalef could be combined as
        glScalef(1,-1,0.5);

    7)  Has this topic been discussed elsewhere?

        RESOLVED:  Yes, see:

        "Maximizing Depth Buffer Range and Precision"
        Brano Kemen
        http://outerra.blogspot.co.uk/2012/11/maximizing-depth-buffer-range-and.html
        November 28, 2012

        "Minimum Triangle Separation for Correct Z-Buffer"
        Kurt Akeley and Jonathan Su
        http://research.microsoft.com/apps/pubs/default.aspx?id=79213
        August 2006

        "Tightening the Precision of Perspective Rendering"
        Paul Upchurch and Mathieu Desbrun
        http://www.geometry.caltech.edu/pubs/UD12.pdf
        Journal of Graphics Tools, Volume 16, Issue 1, 2012.

    8)  How does this extension interact with the unclamped depth range
        parameters of NV_depth_buffer_float's glDepthRangedNV and OpenGL
        4.3?

        RESOLVED:  Simply apply the equations as specified.

        The implications of this are explored...

        An unclamped depth range applies to floating-point depth buffers.

        (For a conventional [0,1] fixed-point depth buffer, the depth
        range is clamped to "the range appropriate to the depth buffer's
        representation."  In practice, this means that unclamped depth
        values are clamped to the [0,1] range when used with a
        conventional depth buffer so are effectively still clamped.)

        If an application were to mix the two like this:

          glDepthRangedNV(-1,1);
          glClipControl(GL_LOWER_LEFT, GL_ZERO_TO_ONE);

        this would lead to generating interpolated depth values in a
        [-1,+1] range.  Because floating-point has more precision in the
        neighborhood of zero, the depth buffer precision is concentrated
        at zero in window-space Z.  This corresponds to 0.5 in normalized
        device coordinates.

        Consider if our projection matrix mapped eye-space 2 to
        clip-space 0.0 and eye-space 1000 to 1.0 with the Z matrix row:

           [  0   0   (n+f)/(n-f)   f*n/(n-f)  ]

        so that

            Zc = -0.5 = 0*x_e + 0*y_e + ((2+1000)/(2-1000))*z_e + (2*1000/(2-1000))*w_e

        solving for z_e when w_e is one, means z_e equals -1.498

        OpenGL 4.3 made a slightly incompatible change in the parameter
        types for glDepthRange (and related commands) from clamped
        floating-point types (GLclampd) to unclamped floating-point
        types (GLdouble).  Hence the functionality of glDepthRangedNV
        also applies to OpenGL 4.3 in the case of floating-point depth
        buffers.

    9)  Can an application be guaranteed the exact same pixels being
        rasterized when the clip control origin is GL_UPPER_LEFT versus
        GL_LOWER_LEFT, except having the scanlines reversed?

        RESOLVED:  No such rasterization invariance is reasonable to
        guarantee.  Slight pixel variances are possible.

        The polygon rasterization rules for OpenGL (section 14.6.1,
        "Polygon Rasterization") states: In such a case [fragment's center
        lies on a polygon boundary edge] we require that if two polygons
        lie on either side of a common edge (with identical endpoints)
        on which a fragment center lies, then exactly one of the polygons
        results in the production of the fragment during rasterization."

        The specification leaves it to implementations to define the
        exact edge rule in this case.  If the sense of Y in clip space
        is flipped, this rule may be decided differently.

        This is further complicated by multisampling where the sample pattern
        is unlikely to be mirrored in the Y direction.

        These issues are razor's edge cases and should not be an issue
        for real applications.

    10) Are all the possible combinations of glClipControl useful?

        RESOLVED: Yes, the initial state (GL_LOWER_LEFT/
        GL_NEGATIVE_ONE_TO_ONE) corresponds to OpenGL's traditional
        behavior.

        The state GL_LOWER_LEFT/GL_ZERO_TO_ONE corresponds to OpenGL's
        traditional origin and Direct3D's depth mode.

        The state GL_UPPER_LEFT/GL_ZERO_TO_ONE corresponds to Direct3D's
        clip volume definition.

        The state GL_UPPER_LEFT/GL_NEGATIVE_ONE_TO_ONE is consistent with
        the upper-left origin of the window coordinate system of Microsoft
        Windows and the X Window System.

    11) Should all the possible combinations of glClipControl
        parameters supported be supported?

        RESOLVED:  Yes, all the combinations should be supported.  The cost
        is low and this provides orthogonality.

        So it is legal to call:

            glClipControl(GL_UPPER_LEFT, GL_NEGATIVE_ONE_TO_ONE);

    12) Does setting the clip control origin to GL_UPPER_LEFT change the
        origin of the window coordinate system use for commands such as
        glViewport, glScissor, glWindowPos2i, and glReadPixels?

        RESOLVED:  No.

        The (x,y) window space location passed to these commands have the
        (0,0) origin at the lower left corner of the window, independent
        of the state of the clip control origin.

        So, for example, an application wanting an Direct3D upper-left orign
        specifying the scissor with upper-left (x,y) coordinates would call:

            glScissor(upper_left_x,
                      window_height - upper_left_y,
                      window_width, window_height);

        The rationale for this choice is to avoid confusion for how
        window space coordinates are passed to commands.  When rendering
        to resizable windows, the window width and height can change
        asychronously.  This would mean the scissor command would need
        to specify a "gravity" for the window origin.  There would also
        need to be a way to "query" this state relative to difference
        origin conventions and subject asynchronous window resizes.

        Moreover, this extension is not changing how window space is
        specified but rather how clip space is specified.

    13) Does the polygon stipple orientation change when the clip control
        origin is set to GL_UPPER_LEFT?

        RESOLVED:  No.

    14) Will using the GL_ZERO_TO_ONE clip control depth mode improve
        my depth precision?

        RESOLVED:  Yes, if you use a floating-point depth buffer and
        place the near and far values at 1.0 and 0.0 (reversed from the
        normal convention).

        But not much if you use a conventional fixed-point depth buffer.

        This really depends on whether the particular hardware
        implementation can numerically improve its depth interpolation
        result.  This depends on a lot of things including the quality
        of the depth plane equation setup, the number of bits of
        sub-pixel precision available, and how the depth interpolation
        is performed.

        With a conventional 24-bit fixed-point depth buffer, applications
        may be able to achieve half a least significant bit (LSB) of
        improved depth buffer precision.

        There are typically far better strategies for improving depth
        precision such as W-buffering, avoiding concatenation of the
        modelview and projection matrices, and (probably the easiest)
        better managing your scene's near and far planes.

        With a floating-point depth buffer, it is more likely the
        GL_ZERO_TO_ONE depth mode will improve depth precision.
        Unfortunately in the conventional depth range [0,1], the
        improvement is primarily close to the near plane where there
        is already excessive precision.  Reversing the depth range with
        the command

            glDepthRange(1.0, 0.0);

        effectively reverses the near and far values in the depth
        buffer.  Also remember to reverse the depth function; so
        glDepthFunc(GL_LESS) should become glDepthRange(GL_GREATER).
        However, this involves computing 1-Z which effectively truncates
        far values (for much the same reason adding +0.5 does).

        Alternatively, the reversal of near and far can happen as part
        of the projection transformation so the depth range specified
        with glDepthRange can be the conventional range [0,1].  Arguably
        folding the near and far reversal into the projection matrix is
        slightly better than reversing the depth range.  However the
        problem remains that a very large value is added with a small
        value close to the far plane so effective depth precision is
        not substantially improved with a fixed-point depth buffer but
        has a substantial advantage for a floating-point depth buffer.

    15) How does this extension interact with geometry shaders?

        RESOLVED:  If there is a geometry shader active, it is the
        geometry shader which is actually writing the clip space position
        (not the vertex shader).

        One way to implement this extension (ignoring geometry shaders
        for now) would be to add an epilogue to the application's vertex
        shader to invert the clip space Y output when the clip control
        origin is GL_UPPER_LEFT and perform a scale by 2 and bias by negative
        clip space W to the clip space Z (biasing by negative clip space
        W is like subtracting 1 in normalized device coordinates).

        However, this epilogue would need to be moved to the geometry
        shader if a geometry shader was active.

    16) How does this extension interact with tessellation evaluation
        shaders (without a geometry shader)?

        RESOLVED:  Then the epilogue discussed in issue #15 would need to
        be added to the tessellation evaluation shader (and not the vertex
        shader since it is really transforming patch control points).

        If there was a geometry shader active, the geometry shader is
        where the epilogue would be done.

    17) Does the discussion of the use an epilogue in the last two issues
        mean using the GL_UPPER_LEFT or GL_ZERO_TO_ONE modes is
        necessarily slower?

        RESOLVED:  Generally no.

        GPUs that support Direct3D are expected to have a mode to support
        GL_UPPER_LEFT and GL_ZERO_TO_ONE at full speed and OpenGL
        implementations for such GPUs should operate at full speed.

    18) Should the clip control state be changed frequently?

        RESOLVED:  Most applications are expected to set the clip control
        conventions once; for example, to match the Direct3D conventions.

        Some implementations may introduce a flush when changing the
        clip control state.  Hence frequent clip control changes are
        not recommended.

        No flush is explicitly required when the clip control changes
        and some implementations (NVIDIA) will have no significant
        performance penalty for changing the clip control state.

    19) Issue #6 addresses fixed-function vertex processing adjustments
        under different clip control modes.  How would a GLSL vertex
        shader be adjusted, assuming how the shader computes its
        clip-space position does not change, for different clip control
        conventions?

        RESOLVED:  The following GLSL epilogues could be added...

        If the clip control origin is GL_UPPER_LEFT, you could add a final
        operation to negate the clip-space Y component.  So:

           gl_Position.y *= -1;

        If the clip control depth mode is GL_ZERO_TO_ONE, you
        could scale and bias the conventional [-1,+1] range of
        normalized-device-coordinate-space Z to the [0,1] range like
        this:

           gl_Position.z = 0.5*gl_Positon.z + 0.5*gl_Position.w;

        Because

           z_ndc = z_c / w_c

        so the epilogue above computes an adjusted z_ndc':

           z_ndc' = (0.5*z_c + 0.5+w_c)/w_c

        which is the same as:

           z_ndc' = 0.5*z_c/w_c + 0.5
                  = 0.5*z_ndc + 0.5

        and scaling a [-1,+1] range by 0.5 and biasing by 0.5 computes
        a linear mapping to the range [0,1].

        Alternatively, rather than adding an epilogue as described,
        the adjustments above could be folded into the transform matrix
        typically used to transform object-space to clip-space.  This is
        a faster approach since it avoids extra math operations in the
        vertex shaders.

    20) Explain the numerical advantage for potential increased depth
        precision for the GL_ZERO_TO_ONE clip control depth mode.

        RESOLVED:  If the normal depth range sets near to 0.0 and far
        to 1.0, this means the effective viewport transform for Z (see
        section 13.6.1 "Controlling the Viewport") becomes an identity
        mapping.  So the mapping in GL_ZERO_TO_ONE depth mode is:

            z_w = (f-n)  * z_d + n

        and when near (n) is 0.0 and far (f) is 1.0, this becomes simply:

           z_w = z_d;

        This identity mapping results in no lose or change in the
        per-vertex window space position.

        Contrast this with the same situation with the
        GL_NEGATIVE_ONE_TO_ONE depth mode with the mapping:

           z_w =  (f-n)/2 * z_d + (n+f)/2

        and when near (n) is 0.0 and far (f) is 1.0, this becomes simply:

           z_w = 0.5 * z_d + 0.5

        While multiplying z_d by 0.5 has no precision loss (ignoring
        denorms, this scale simply decrements the exponent by 1 without
        disturbing the mantissa).  However a bias by 0.5 does distrurb
        the floating-point precision (also see Issue #3), losing one
        least-significant-bit (LSB) of precision.

    21) What should the state to control the GL_NEGATIVE_ONE_TO_ONE
        and GL_ZERO_TO_ONE convention be called?

        RESOLVED:  GL_CLIP_DEPTH_MODE.

        An alternative would be GL_CLIP_Z_MODE but the convention
        is well-established in the OpenGL API that Z values that are
        interpreted as depth values are described as DEPTH.

    22) Direct3D 8 and 9 have a window-space coordinate system where
        pixel centers are centered on integer coordinates.  OpenGL
        (and Direct3D 10 and 11) position pixel centers at half-pixel
        locations.  Should ARB_clip_control account for the older Direct3D
        integer pixel center convention?

        RESOLVED:  No, because existing functionality covers this...

        The EXT_viewport_array extension (made a core part of OpenGL
        with version 4.1) extends the viewport state to be specified as
        floating-point (technically fixed-point) values.  Prior to this
        extension, the viewport parameters were integral.

        With the EXT_viewport_array functionality, you can add a bias of
        (0.5,0.5) to the viewport (x,y) to shift integer Direct3D 8/9
        style window space locations to OpenGL's half-pixel convention.

        If you had a Direct3D upper-left viewport (x,y), you'd match
        the Direct3D clip-space AND window-space conventions like this:

            glClipControl(GL_UPPER_LEFT, GL_ZERO_TO_ONE);
            const GLuint viewport_index = 0;  // Prior to DirectX 10, there's only a single viewport
            glViewportIndexedf(viewport_index,
                x + 0.5f, window_height - (y + view_height) + 0.5f,
                view_width, view_height);

        where window_height is the height of the window/surface in pixels.

        Also note the EXT_fragment_coord_conventions (made a core part
        of OpenGL with version 3.2) allows the window position varying
        input to fragment shaders to reflect the Direct3D 9 window-space
        convention.  See that extension for details.

    23) Does this extension's state affect user clip planes?

        RESOLVED:  No, user clip planes operate on eye-space coordinates
        which are not affected by this extension's state.

    24) Does this extension's state affect fixed-function fog?

        RESOLVED:  No, fixed-function fog operates on eye-space distance
        which is not affected by this extension's state.

    25) Does this extension's state affect the point sprite origin?

        RESOLVED:  No.

        When the EXT_point_sprite functionality was promoted to a core
        feature in OpenGL 2.0, the GL_POINT_SPRITE_ORIGIN state was added
        to specify whether the 2D texture coordinate has a lower-left
        (OpenGL's convention in EXT_point_sprite and NV_point_sprite)
        or upper-left (Direct3D convention).

        An application wanting to emulate Direct3D's upper-left point
        sprite texture coordinate origin should change the origin state
        with an explicit point parameter command.  Specifically:

            glPointParameteri(GL_POINT_SPRITE_ORIGIN, GL_UPPER_LEFT);

        This command is in addition to calling glClipControl and
        specifying a GL_UPPER_LEFT origin.

    26) Issue #12 says the origin for glWindowPos2i and other glWindowPos*
        commands is lower-left independent of the clip control state.
        What about glRasterPos2i and other glRasterPos* commands?

        RESOLVED:  Yes, the raster position specified by glRasterPos2i,
        etc.  is affected by the clip control state because the
        object-space position is transformed and clipped just as a point
        vertex position would be to arrive at the clip-space raster
        position that is further transformed to window space.

    27) Is the depth value specified for glClearDepth affected by this
        extension's clip control state?

        RESOLVED:  No, glClearDepth takes a window-space depth value.

        This extension only affects how clip space clipping and the
        transformation from clip space to window space operates.

        Likewise depth values read (glReadPixels), drawn (glDrawPixels),
        or copied (glCopyPixels, glBlitFramebuffer) are unaffected by
        this extension's clip control state.

    28) Does this extension's state affect the operation of polygon
        offset?

        RESOLVED:  No, polygon offset operates on window-space depth
        values.  This extension's clip control state operates prior
        to polygon offset.

    29) Can glClipControl be display listed?

        RESOLVED:  Yes.

    30) Should the command be glClipParameteri to anticipate more
        control of clipping state?

        RESOLVED:  No.  Given over 20 years with basically zero extensions
        in the area of clipping state, we realistically don't anticipate
        more clipping parameters.  Even in the case of this extension, the
        rationale for this extension is quite limited and not about adding
        any "features" to clipping.  Instead the purpose is simply to
        match the conventions of Direct3D (not a functional change).
        While Direct3D's convention is different from OpenGL, there
        simply aren't any futher 3D APIs or standards which clip
        differently.

        Also glClipControl maintains consistency with the existing
        glClipPlane command pattern for the clipping API.

        Historically "Parameter" has been used for commands that affect
        managed "object" state and/or have a speciailized "Get" query
        command (glGetColorTableParameter*) rather than fixed-function
        pipeline state.  This isn't completely uniform (exceptions:
        point parameters, patch parameters) but the vast majority of
        fixed-function rendering state isn't set with gl*Parameter
        style commands.  When "Parameter" commands are used there
        is typically a plurality of state settings with different
        integer/float/double/boolean types.  None of the situations
        that justify gl*Parameter style commands are present in this
        extension.

    31) This extension is only useful if it is widely available.  So how
        easy would this extension be to implement?

        RESOLVED:  No special hardware is required due to the careful
        way this extension is specified.  The clip control functionality
        could all be done by inexpensive epilogue math appended to the
        last shader in the graphics pipeline.  The Y inversion could be
        performed as part of the viewport transform.

        Given the prevalance of Direct3D-capable hardware, we expect
        some hardware vendors will implement this extension with
        special existing modes in their hardware to handle the Direct3D
        conventions.  However we emphasize no special hardware is required
        and the performance benefit attributable to such hardware is
        likely to be extremely meager.

        With respect to Mesa3D and Gallium, Brian Paul observes:  "This
        extension should be pretty easy to implement in Mesa/gallium.
        In Gallium we already have a state variable for Z 0/1 vs. -1/+1
        clipping.  And I think we could implement the Y origin via our
        viewport state (which is specified in floats)."

    32) Is support for the GL_UPPER_LEFT convention just to match
        Direct3D/Windows?

        RESOLVED:  No.  Along with Windows/Direct3D/Direct2D, X11 and
        Java also have upper-left graphics device coordinate systems.

        OpenGL, PostScript, PHIGS, GKS, and Apple's Core Graphics
        (Quartz 2D) have lower-left graphics device coordinate systems.

    33) When rendering to off-screen framebuffer objects (FBOs) that
        will subsequently be textured from, how do I make sure the texture
        coordinate origin and the window space origin are consistent?

        RESOLVED:  Use GL_LOWER_LEFT for the origin parameter of
        glClipControl in this case.  Use the GL_UPPER_LEFT for the
        origin parameter when matching Direct3D's origin *and* drawing
        into a window framebuffer to be directly presented.

    34) Can you provide an example illustrating how applications using the
        coordinate system conventions of Direct3D map onto this extension?

        RESOLVED:  Consider a Direct3D application rendering a triangle ABC
        (with counter-clockwise orientation) to a viewport in the upper-left
        quadrant of the destination surface.  The surface (with Direct3D
        window coordinates) is illustrated here.

            (0,0)         (960,0)          (1920,0)
            +------(A)-------+----------------+
            |^ Y_c == +W_c ^ |                |
            |                |                |
            |                |                |
            |                |                |
            |v Y_c == -W_c v |                |
            +-(B)--------(C)-+----------------+
            |                |                |
            |                |                |
            |                |                |
            |                |                |
            |                |                |
            +----------------+----------------+
            (0,1080)                      (1920,1080)

        In this example, assume vertices A, B, and C have clip coordinates of:

          A = (+0.0, +1.0, +0.5, +1.0)
          B = (-0.8, -1.0, +0.5, +1.0)
          C = (+0.8, -1.0, +0.5, +1.0)

        Direct3D's coordinate transformations are functionally similar to
        OpenGL's, except that (a) the Y coordinate is inverted as part of the
        viewport transformation mapping normalized device coordinates (NDCs)
        to window coordinates and (b) the depth range transformation maps Z==0
        to the near value instead of halfway between near and far as in
        OpenGL:

          http://msdn.microsoft.com/en-us/library/windows/desktop/
          bb206341%28v=vs.85%29.aspx

        Because of the Y inversion from (a), vertices in Direct3D with a Y NDC
        of -1.0 map to the bottom of the viewport (larger Y window coordinates
        in the Direct3D coordinate system).  This is exactly like OpenGL
        windowed rendering, where a Y NDC of -1 maps to smaller Y window
        coordinates (bottom) in the OpenGL coordinate system.  Thanks to this
        inversion in the Direct3D viewport transformation, rendering a
        Direct3D scene with the same coordinates and matrices in OpenGL will
        produce an image with identical vertical orientation and winding
        (CW/CCW).  However, since the viewport rectangle itself is programmed
        in window coordinates, a Direct3D-centric viewport of (0,0,960,540)
        needs to be flipped to (0,540,960,540) to work in OpenGL.
        Additionally, to get identical near/far clipping and Z values, it's
        necessary to use the ZERO_TO_ONE mode in this extension to have OpenGL
        process Z coordinates identically to Direct3D.

        When rendering to off-screen surfaces later used as textures, the
        issue is a little bit more complex.  A Direct3D application will use
        the texture coordinates (0,0) to refer to the upper left corner of the
        upper leftmost pixel of the image.  However, in OpenGL, texture
        coordinates of (0,0) refer to the lower-left corner of the
        lower-leftmost pixel of the image.  One way to compensate for this is
        to remap the <t> texture coordinate with:

          t_OpenGL = 1.0 - t_Direct3D

        Unfortunately, that requires a modification to shaders or other input
        data in the application.  Instead of doing this, the UPPER_LEFT mode
        in this extension provides a simple way to use Direct3D texture
        coordinate conventions -- by rendering the entire scene *upside-down*
        from the point of view of OpenGL.  The image we want to produce using
        this technique (below) is a vertically inverted version of the
        previous image, where OpenGL lower-left window coordinates are
        depicted in the figure.

            (0,1080)                      (1920,1080)
            +----------------+----------------+
            |                |                |
            |                |                |
            |                |                |
            |                |                |
            |                |                |
            +-(B)--------(C)-+----------------+
            |v Y_c == -W_c v |                |
            |                |                |
            |                |                |
            |                |                |
            |^ Y_c == +W_c ^ |                |
            +------(A)-------+----------------+
            (0,0)         (960,0)          (1920,0)

        In this example, the UPPER_LEFT mode in this extension inverts the
        geometry as part of the transformation from clip coordinates to NDCs,
        so that vertex A has a Y NDC of -1.0 instead of +1.0.  This puts A at
        the bottom of the viewport, while B and C remain at the top.  One
        thing to note is that the inversion changes the orientation of
        triangle ABC, which is now clockwise instead of counter-clockwise.  To
        compensate, this extension also inverts the value computed to compute
        face direction when in UPPER_LEFT mode.  The one other thing to note
        here is that when rendering this way, the Direct3D viewport should be
        used as-is in OpenGL.

        Note that a similar inversion technique can be used to implement
        OpenGL FBO rendering on graphics hardware supporting only Direct3D
        coordinate systems.  If this technique is used on an implementation
        doing something like this, the two inversions cancel each other out.

Revision History

    Rev.    Date    Author     Changes
    ----  -------- ---------  ----------------------------------------------
    3     04/26/13 mjk        Add issues 15 to 21
                              Change CLIP_Z_MODE to CLIP_DEPTH_MODE
    4     04/30/13 mjk        Add issue 22
    5     05/01/13 mjk        Add issues 22 to 28, fix typos
    6     05/09/13 mjk        Add issue 29 to 31
    7     05/13/13 pdaniell   Internal revisions
    8     05/13/13 mjk        Valve feedback; change to KHR in issues
    9     05/13/13 mjk        Change to KHR in issues
    10    05/28/13 pdaniell   Fold in feedback from Mark Callow in bug 10245
    11    05/30/13 pdaniell   Internal revisions
    12    06/06/13 pdaniell   Internal revisions
    13    06/17/13 pdaniell   Fix the enum token values
    14    07/03/13 mjk        D3D off-screen discussion; issue 32 and 33
    15    04/16/14 pdaniell   Prepare spec for OpenGL 4.5
    16    04/17/14 pdaniell   Fixes "UPPER_RIGHT" typos to UPPER_LEFT
    17    07/30/14 pbrown     Fix incorrect language in the overview
                              describing when to use UPPER_LEFT and LOWER_LEFT
                              modes; add detailed examples in issue 34.
    18    09/17/15 Jon Leech  Correct typo in issue 7 and add contributor
                              Brano Kemen from that issue.