Question
I'm working on porting from OpenGL (OGL) to MetalKit (MTK) on iOS. I'm failing to get identical display in the MetalKit version of the app. I modified the projection matrix to account for differences in Normalized Device Coordinates between the two frameworks, but don't know what else to change to get identical display. Any ideas what else needs to be changed to port from OpenGL to MetalKit?
Projection Matrix Changes so far...
I understand that the Normalized Device Coordinates (NDC) are different in OGL vs MTK:
OGL NDC: -1 < z < 1
MTK NDC: 0 < z < 1
I modified the projection matrix to address the NDC difference, as indicated here. Unfortunately, this modification to the projection matrix doesn't result in identical display to the old OGL code.
I'm struggling to even know what else to try.
Background
For reference, here's some misc background information:
The view matrix is very simple (identity matrix); i.e. camera is at (0, 0, 0) and looking toward (0, 0, -1)
In the legacy OpenGL code, I used GLKMatrix4MakeFrustum to produce the projection matrix, using the screen bounds for left, right, top, bottom, and near=1, far=1000
I stripped the scene down to bare bones while debugging and below are 2 images, the first from legacy OGL code and the second from MTK, both just showing the "ground" plane with a debug texture and a black background.
Any ideas about what else might need to change to get to identical display in MetalKit would be greatly appreciated.
Screenshots
OpenGL (legacy)
MetalKit
Edit 1
I tried to extract code relevant to calculation and use of the projection matrix:
float aspectRatio = 1.777; // iPhone 8 device
float top = 1;
float bottom = -1;
float left = -aspectRatio;
float right = aspectRatio;
float RmL = right - left;
float TmB = top - bottom;
float nearZ = 1;
float farZ = 1000;
GLKMatrix4 projMatrix = { 2 * nearZ / RmL, 0, 0, 0,
0, 2 * nearZ / TmB, 0, 0,
0, 0, -farZ / (farZ - nearZ), -1,
0, 0, -farZ * nearZ / (farZ - nearZ), 0 };
GLKMatrix4 viewMatrix = ...; // Identity matrix: camera at origin, looking at (0, 0, -1), yUp=(0, 1, 0);
GLKMatrix4 modelMatrix = ...; // Different for various models, but even when this is the identity matrix in old/new code the visual output is different
GLKMatrix4 mvpMatrix = GLKMatrix4Multiply(projMatrix, GLKMatrix4Multiply(viewMatrix, modelMatrix));
...
GLKMatrix4 x = mvpMatrix; // rename for brevity below
float mvpMatrixArray[16] = {x.m00, x.m01, x.m02, x.m03, x.m10, x.m11, x.m12, x.m13, x.m20, x.m21, x.m22, x.m23, x.m30, x.m31, x.m32, x.m33};
// making MVP matrix available to vertex shader
[renderCommandEncoder setVertexBytes:&mvpMatrixArray
length:16 * sizeof(float)
atIndex:1]; // vertex data is at "0"
[renderCommandEncoder setVertexBuffer:vertexBuffer
offset:0
atIndex:0];
...
[renderCommandEncoder drawPrimitives:MTLPrimitiveTypeTriangleStrip
vertexStart:0
vertexCount:4];
Sadly this issue ended up being due to a bug in the vertex shader that was pushing all geometry +1 on the Z axis, leading to the visual differences.
For any future OpenGL-to-Metal porters: the projection matrix changes above, accounting for the differences in normalized device coordinates, are enough.
Without seeing the code it's hard to say what the problem is. One of the most common issues could be a wrongly configured viewport:
// Set the region of the drawable to draw into.
[renderEncoder setViewport:(MTLViewport){0.0, 0.0, _viewportSize.x, _viewportSize.y, 0.0, 1.0 }];
The default values for the viewport are:
originX = 0.0
originY = 0.0
width = w
height = h
znear = 0.0
zfar = 1.0
*Metal: znear = minZ, zfar = maxZ.
MinZ and MaxZ indicate the depth-ranges into which the scene will be
rendered and are not used for clipping. Most applications will set
these members to 0.0 and 1.0 to enable the system to render to the
entire range of depth values in the depth buffer. In some cases, you
can achieve special effects by using other depth ranges. For instance,
to render a heads-up display in a game, you can set both values to 0.0
to force the system to render objects in a scene in the foreground, or
you might set them both to 1.0 to render an object that should always
be in the background.
Applications typically set MinZ and MaxZ to 0.0 and 1.0 respectively
to cause the system to render to the entire depth range. However, you
can use other values to achieve certain affects. For example, you
might set both values to 0.0 to force all objects into the foreground,
or set both to 1.0 to render all objects into the background.
Related
I am currently studying shadow mapping, and my biggest issue right now is the transformations between spaces. This is my current working theory/steps.
Pass 1:
Get depth of pixel from camera, store in depth buffer
Get depth of pixel from light, store in another buffer
Pass 2:
Use texture coordinate to sample camera's depth buffer at current pixel
Convert that depth to a view space position by multiplying the projection coordinate with invProj matrix. (also do a perspective divide).
Take that view position and multiply by invV (camera's inverse view) to get a world space position
Multiply world space position by light's viewProjection matrix.
Perspective divide that projection-space coordinate, and manipulate into [0..1] to sample from light depth buffer.
Get current depth from light and closest (sampled) depth, if current depth > closest depth, it's in shadow.
Shader Code
Pass1:
PS_INPUT vs(VS_INPUT input) {
output.pos = mul(input.vPos, mvp);
output.cameraDepth = output.pos.zw;
..
float4 vPosInLight = mul(input.vPos, m);
vPosInLight = mul(vPosInLight, light.viewProj);
output.lightDepth = vPosInLight.zw;
}
PS_OUTPUT ps(PS_INPUT input){
float cameraDepth = input.cameraDepth.x / input.cameraDepth.y;
//Bundle cameraDepth in alpha channel of a normal map.
output.normal = float4(input.normal, cameraDepth);
//4 Lights in total -- although only 1 is active right now. Going to use r/g/b/a for each light depth.
output.lightDepths.r = input.lightDepth.x / input.lightDepth.y;
}
Pass 2 (Screen Quad):
float4 ps(PS_INPUT input) : SV_TARGET{
float4 pixelPosView = depthToViewSpace(input.texCoord);
..
float4 pixelPosWorld = mul(pixelPosView, invV);
float4 pixelPosLight = mul(pixelPosWorld, light.viewProj);
float shadow = shadowCalc(pixelPosLight);
//For testing / visualisation
return float4(shadow,shadow,shadow,1);
}
float4 depthToViewSpace(float2 xy) {
//Get pixel depth from camera by sampling current texcoord.
//Extract the alpha channel as this holds the depth value.
//Then, transform from [0..1] to [-1..1]
float z = (_normal.Sample(_sampler, xy).a) * 2 - 1;
float x = xy.x * 2 - 1;
float y = (1 - xy.y) * 2 - 1;
float4 vProjPos = float4(x, y, z, 1.0f);
float4 vPositionVS = mul(vProjPos, invP);
vPositionVS = float4(vPositionVS.xyz / vPositionVS.w,1);
return vPositionVS;
}
float shadowCalc(float4 pixelPosL) {
//Transform pixelPosLight from [-1..1] to [0..1]
float3 projCoords = (pixelPosL.xyz / pixelPosL.w) * 0.5 + 0.5;
float closestDepth = _lightDepths.Sample(_sampler, projCoords.xy).r;
float currentDepth = projCoords.z;
return currentDepth > closestDepth; //Supposed to have bias, but for now I just want shadows working haha
}
CPP Matrices
// (Position, LookAtPos, UpDir)
auto lightView = XMMatrixLookAtLH(XMLoadFloat4(&pos4), XMVectorSet(0,0,0,1), XMVectorSet(0,1,0,0));
// (FOV, AspectRatio (1000/680), NEAR, FAR)
auto lightProj = XMMatrixPerspectiveFovLH(1.57f , 1.47f, 0.01f, 10.0f);
XMStoreFloat4x4(&_cLightBuffer.light.viewProj, XMMatrixTranspose(XMMatrixMultiply(lightView, lightProj)));
Current Outputs
White signifies that a shadow should be projected there. Black indicates no shadow.
CameraPos (0, 2.5, -2)
CameraLookAt (0, 0, 0)
CameraFOV (1.57)
CameraNear (0.01)
CameraFar (10.0)
LightPos (0, 2.5, -2)
LightLookAt (0, 0, 0)
LightFOV (1.57)
LightNear (0.01)
LightFar (10.0)
If I change the CameraPosition to be (0, 2.5, 2), basically just flipped on the Z axis, this is the result.
Obviously a shadow shouldn't change its projection depending on where the observer is, so I think I'm making a mistake with the invV. But I really don't know for sure. I've debugged the light's projView matrix, and the values seem correct - going from CPU to GPU. It's also entirely possible I've misunderstood some theory along the way because this is quite a tricky technique for me.
Aha! Found my problem. It was a silly mistake, I was calculating the depth of pixels from each light, but storing them in a texture that was based on the view of the camera. The following image should explain my mistake better than I can with words.
For future reference, the solution I decided was to scrap my idea for storing light depths in texture channels. Instead, I basically make a new pass for each light, and bind a unique depth-stencil texture to render the geometry to. When I want to do light calculations, I bind each of the depth textures to a shader resource slot and go from there. Obviously this doesn't scale well with many lights, but for my student project where I'm only required to have 2 shadow casters, it suffices.
_context->DrawIndexed(indexCount, 0, 0); //Draw to regular render target
_sunlight->use(1, _context); //Use sunlight shader (basically just runs a Vertex Shader & Null Pixel shader so depth can be written to depth map)
_sunlight->bindDSVSetNullRenderTarget(_context);
_context->DrawIndexed(indexCount, 0, 0); //Draw to sunlight depth target
bindDSVSetNullRenderTarget(ctx){
ID3D11RenderTargetView* nullrv = { nullptr };
ctx->OMSetRenderTargets(1, &nullrv, _sunlightDepthStencilView);
}
//The purpose of setting a null render target before doing the draw call is
//that a draw call with only a depth target bound is much faster.
//(At least I believe so, from my reading online)
So I've been working on a Directx11/hlsl rendering engine with the goal of creating a realistic planet which you can view from both on the surface and also at a planetary level. The planet is a normalized cube, which is procedurally generated using noise and as you move closer to the surface of the planet, a binary-based triangle tree splits until the desired detail level is reached. I got vertex normal calculations to work correctly, and I recently started trying to implement normal mapping for my terrain textures, and I have gotten something that seems to work for the most part. However, when the sun is pointing almost perpendicular to the ground (90 degrees), it is way more lit up
However, from the opposite angle (270 degrees), I am getting something that seems
, but may as well be just as off.
The debug lines that are being rendered are the normal, tangent, and bitangents (which all appear to be correct and fit the topology of the terrain)
Here is my shader code:
Vertex shader:
PSIn mainvs(VSIn input)
{
PSIn output;
output.WorldPos = mul(float4(input.Position, 1.f), Instances[input.InstanceID].WorldMatrix); // pass pixel world position as opposed to screen space position for lighitng calculations
output.Position = mul(output.WorldPos, CameraViewProjectionMatrix);
output.TexCoord = input.TexCoord;
output.CameraPos = CameraPosition;
output.Normal = normalize(mul(input.Normal, (float3x3)Instances[input.InstanceID].WorldMatrix));
float3 Tangent = normalize(mul(input.Tangent, (float3x3)Instances[input.InstanceID].WorldMatrix));
float3 Bitangent = normalize(cross(output.Normal, Tangent));
output.TBN = transpose(float3x3(Tangent, Bitangent, output.Normal));
return output;
}
Pixel shader (Texcoord scalar is for smaller textures closer to planet surface):
float3 FetchNormalVector(float2 TexCoord)
{
float3 Color = NormalTex.Sample(Samp, TexCoord * TexcoordScalar);
Color *= 2.f;
return normalize(float3(Color.x - 1.f, Color.y - 1.f, Color.z - 1.f));
}
float3 LightVector = -SunDirection;
float3 TexNormal = FetchNormalVector(input.TexCoord);
float3 WorldNormal = normalize(mul(input.TBN, TexNormal));
float nDotL = max(0.0, dot(WorldNormal, LightVector));
float4 SampleColor = float4(1.f, 1.f, 1.f, 1.f);
SampleColor *= nDotL;
return float4(SampleColor.xyz, 1.f);
Thanks in advance, and let me know if you have any insight as to what could be the issue here.
Edit 1: I tried it with a fixed blue value instead of sampling from the normal texture, which gives me the correct and same results as if I had not applied mapping (as expected). Still don't have a lead on what would be causing this issue.
Edit 2: I just noticed the strangest thing. At 0, 0, +Z, there are these hard seams that only appear with normal mapping enabled
It's a little hard to see, but it seems almost like there are multiple tangents associated to the same vertex (since I'm not using indexing yet) because the debug lines appear to split on the seams.
Here is my code that I'm using to generate the tangents (bitangents are calculated in the vertex shader using cross(Normal, Tangent))
v3& p0 = Chunk.Vertices[0].Position;
v3& p1 = Chunk.Vertices[1].Position;
v3& p2 = Chunk.Vertices[2].Position;
v2& uv0 = Chunk.Vertices[0].UV;
v2& uv1 = Chunk.Vertices[1].UV;
v2& uv2 = Chunk.Vertices[2].UV;
v3 deltaPos1 = p1 - p0;
v3 deltaPos2 = p2 - p0;
v2 deltaUV1 = uv1 - uv0;
v2 deltaUV2 = uv2 - uv0;
f32 r = 1.f / (deltaUV1.x * deltaUV2.y - deltaUV1.y * deltaUV2.x);
v3 Tangent = (deltaPos1 * deltaUV2.y - deltaPos2 * deltaUV1.y) * r;
Chunk.Vertices[0].Tangent = Normalize(Tangent - (Chunk.Vertices[0].Normal * DotProduct(Chunk.Vertices[0].Normal, Tangent)));
Chunk.Vertices[1].Tangent = Normalize(Tangent - (Chunk.Vertices[1].Normal * DotProduct(Chunk.Vertices[1].Normal, Tangent)));
Chunk.Vertices[2].Tangent = Normalize(Tangent - (Chunk.Vertices[2].Normal * DotProduct(Chunk.Vertices[2].Normal, Tangent)));
Also for reference, this is the main article I was looking at while implementing all of this: link
Edit 3:
Here is an image of the planet from a distance with normal mapping enabled:
And one from the same angle without:
I have been working on Pose Estimation (rectifying key points on a 3D model with 2D points on an image to match pose) via OpenCV's cv::solvePNP, using features / key points from Apples Vision framework.
TL-DR:
My scene kit model is being translated and the units look correct when introspecting the translation and rotation vectors from solvePnP (ie, they are the right order of magnitude), but the coordinate system of the translation appears off:
I am trying to understand the coordinate system requirements with solvePnP wrt to Metal / OpenGL coordinate system and my camera projection matrix.
What 'projectionMatrix' does my SCNCamera require to match image based coordinate system passed into solvePnP?
Some things ive read / believe I am taking into account.
OpenCV vs OpenGL (thus Metal) have row major vs column major differences.
OpenCV's coordinate system for 3D is different than OpenGL (thus Metal).
Longer with code:
My workflow is as such:
Step 1 - use a 3D model tool to introspect points on my 3D model and get the objects vertex positions for the major key points in the 2D detected features. I am using left pupil, right pupil, tip of nose, tip of chin, left outer lip corner, right outer lip corner.
Step 2 - Run a vision request and extract a list of points in image space (converting for OpenCV's top left coordinate system) and extract the same ordered list of 2D points.
Step 3 - Construct a camera matrix by using the size of the input image.
Step 4 - run cv::solvePnP, and then use cv::Rodrigues to convert the rotation vector to a matrix
Step 5 - Convert the coordinate system of the resulting transforms into something appropriate for the GPU - invert the y and z axis and combine the translation and rotation to a single 4x4 Matrix, and then transpose it for the appropriate major ness of OpenGL / Metal
Step 6 - apply the resulting transform to Scenekit via:
let faceNodeTransform = openCVWrapper.transform(for: landmarks, imageSize: size)
self.destinationView.pointOfView?.transform = SCNMatrix4Invert(faceNodeTransform)
Below is my Obj-C++ OpenCV Wrapper which takes in a subset of Vision Landmarks and the true pixel size of the image being looked at:
/ https://answers.opencv.org/question/23089/opencv-opengl-proper-camera-pose-using-solvepnp/
- (SCNMatrix4) transformFor:(VNFaceLandmarks2D*)landmarks imageSize:(CGSize)imageSize
{
// 1 convert landmarks to image points in image space (pixels) to vector of cv::Point2f's :
// Note that this translates the point coordinate system to be top left oriented for OpenCV's image coordinates:
std::vector<cv::Point2f > imagePoints = [self imagePointsForLandmarks:landmarks imageSize:imageSize];
// 2 Load Model Points
std::vector<cv::Point3f > modelPoints = [self modelPoints];
// 3 create our camera extrinsic matrix
// TODO - see if this is sane?
double max_d = fmax(imageSize.width, imageSize.height);
cv::Mat cameraMatrix = (cv::Mat_<double>(3,3) << max_d, 0, imageSize.width/2.0,
0, max_d, imageSize.height/2.0,
0, 0, 1.0);
// 4 Run solvePnP
double distanceCoef[] = {0,0,0,0};
cv::Mat distanceCoefMat = cv::Mat(1 ,4 ,CV_64FC1,distanceCoef);
// Output Matrixes
std::vector<double> rv(3);
cv::Mat rotationOut = cv::Mat(rv);
std::vector<double> tv(3);
cv::Mat translationOut = cv::Mat(tv);
cv::solvePnP(modelPoints, imagePoints, cameraMatrix, distanceCoefMat, rotationOut, translationOut, false, cv::SOLVEPNP_EPNP);
// 5 Convert rotation matrix (actually a vector)
// To a real 4x4 rotation matrix:
cv::Mat viewMatrix = cv::Mat::zeros(4, 4, CV_64FC1);
cv::Mat rotation;
cv::Rodrigues(rotationOut, rotation);
// Append our transforms to our matrix and set final to identity:
for(unsigned int row=0; row<3; ++row)
{
for(unsigned int col=0; col<3; ++col)
{
viewMatrix.at<double>(row, col) = rotation.at<double>(row, col);
}
viewMatrix.at<double>(row, 3) = translationOut.at<double>(row, 0);
}
viewMatrix.at<double>(3, 3) = 1.0f;
// Transpose OpenCV to OpenGL coords
cv::Mat cvToGl = cv::Mat::zeros(4, 4, CV_64FC1);
cvToGl.at<double>(0, 0) = 1.0f;
cvToGl.at<double>(1, 1) = -1.0f; // Invert the y axis
cvToGl.at<double>(2, 2) = -1.0f; // invert the z axis
cvToGl.at<double>(3, 3) = 1.0f;
viewMatrix = cvToGl * viewMatrix;
// Finally transpose to get correct SCN / OpenGL Matrix :
cv::Mat glViewMatrix = cv::Mat::zeros(4, 4, CV_64FC1);
cv::transpose(viewMatrix , glViewMatrix);
return [self convertCVMatToMatrix4:glViewMatrix];
}
- (SCNMatrix4) convertCVMatToMatrix4:(cv::Mat)matrix
{
SCNMatrix4 scnMatrix = SCNMatrix4Identity;
scnMatrix.m11 = matrix.at<double>(0, 0);
scnMatrix.m12 = matrix.at<double>(0, 1);
scnMatrix.m13 = matrix.at<double>(0, 2);
scnMatrix.m14 = matrix.at<double>(0, 3);
scnMatrix.m21 = matrix.at<double>(1, 0);
scnMatrix.m22 = matrix.at<double>(1, 1);
scnMatrix.m23 = matrix.at<double>(1, 2);
scnMatrix.m24 = matrix.at<double>(1, 3);
scnMatrix.m31 = matrix.at<double>(2, 0);
scnMatrix.m32 = matrix.at<double>(2, 1);
scnMatrix.m33 = matrix.at<double>(2, 2);
scnMatrix.m34 = matrix.at<double>(2, 3);
scnMatrix.m41 = matrix.at<double>(3, 0);
scnMatrix.m42 = matrix.at<double>(3, 1);
scnMatrix.m43 = matrix.at<double>(3, 2);
scnMatrix.m44 = matrix.at<double>(3, 3);
return (scnMatrix);
}
Some questions:
An SCNNode has no modelViewMatrix (just as I understand it, a transform, which is the modelMatrix) to just throw a matrix at - so I've read the inverse of the transform from SolvePNP process can be used to pose the camera instead, which appears to get me the closes result. I want to ensure this approach is correct.
If I have the modelViewMatrix, and the projectionMatrix, I should be able to calculate the appropriate modelMatrix? Is this the approach I should be taking?
Its unclear to me what projectionMatrix I should be using for my SceneKit Scene and If that has any bearing on my results. Do I need a pixel for pixel exact match of my viewport to the image size, and how do I properly configure my SCNCamera to ensure coordinate system agreeance for SolvePnP?
Thank you very much!
Recently, I jumped in to openGL. Most things have working out quite okay, but I keep banging my head against the wall with this one.
I am trying to rotate/scale an 2D image. I am struggling with the fact it I should rotate first, and then scale, or the other way around. Both ways don't quite work out the way I want.
I have made two short video's showing what it going wrong:
First rotate, then scale
https://dl.dropboxusercontent.com/u/992980/rotate_then_scale.MOV
First scale, then rotate
https://dl.dropboxusercontent.com/u/992980/scale_then_rotate.MOV
The left image is square, the right image is a rectangle. As you can see, with both methods, something is not quite right :)
The black area is the openGL viewport. When the viewport is square, everything is fine, when it is a rectangle, things start to go wrong :) For every image i draw, I calculate a different X and Y scale, in reference to the viewport, I think I am doing something wrong there...
Note that I am quite new to openGL, and I am probably doing something stupid (I hope I am). Hopefully, I can get my question across clearly this way.
Thanks in advance for any help given!
Corjan
The code for drawing one image:
void instrument_renderer_image_draw_raw(struct InstrumentRenderImage* image, struct InstrumentRendererCache* cache, GLuint program) {
// Load texture if not yet done
if (image->loaded == INSTRUMENT_RENDER_TEXTURE_UNLOADED) {
image->texture = instrument_renderer_texture_cache_get(image->imagePath);
if (image->texture == 0) {
image->loaded = INSTRUMENT_RENDER_TEXTURE_ERROR;
}
else {
image->loaded = INSTRUMENT_RENDER_TEXTURE_LOADED;
}
}
// Show image when texture has been correctly loaded into GPU memory
if (image->loaded == INSTRUMENT_RENDER_TEXTURE_LOADED) {
float instScaleX = (float)cache->instBounds.w / cache->instOrgBounds.w;
float instScaleY = (float)cache->instBounds.h / cache->instOrgBounds.h;
float scaleX = (float)image->w / (float)cache->instOrgBounds.w;
float scaleY = (float)image->h / (float)cache->instOrgBounds.h;
// Do internal calculations when dirty
if (image->base.dirty) {
mat4 matScale;
mat4 matRotate;
mat4 matModelView;
mat4 matProjection;
matrixRotateZ(image->angle, matRotate);
matrixScale(scaleX , scaleY * -1, 0, matScale);
matrixMultiply(matRotate, matScale, matModelView);
// Determine X and Y within this instrument's viewport
float offsetX = ((float)cache->instOrgBounds.w - (float)image->w) / 2 / (float)cache->instOrgBounds.w;
float offsetY = ((float)cache->instOrgBounds.h - (float)image->h) / 2 / (float)cache->instOrgBounds.h;
float translateX = ( ((float)image->x / (float)cache->instOrgBounds.w) - offsetX) * 2;
float translateY = ( ( ( (float)cache->instOrgBounds.h - (float)image->y - (float)image->h ) / (float)cache->instOrgBounds.h) - offsetY) * -2;
matrixTranslate(translateX, translateY*-1, -2.4,matModelView);
//matrixPerspective(45.0, 0.1, 100.0, (double)cache->instOrgBounds.w/(double)cache->instOrgBounds.h, matProjection);
matrixOrthographic(-1, 1, -1, 1, matProjection);
matrixMultiply(matProjection, matModelView, image->glMatrix);
image->base.dirty = 0;
}
glUseProgram(program);
glViewport(cache->instBounds.x * cache->masterScaleX,
cache->instBounds.y * cache->masterScaleY,
cache->instBounds.w * cache->masterScaleX,
cache->instBounds.w * cache->masterScaleX);
glUniformMatrix4fv(matrixUniform, 1, GL_FALSE, image->glMatrix);
// Load texture
glBindTexture(GL_TEXTURE_2D, image->texture);
glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
}
What framework/library are you using for matrix multiplication?
The thing that needs to come first depends on your matrix representation (e.g. row- vs. column-major and post- vs. pre-multiplication). The library you use dictates that; fixed-function OpenGL (glMultMatrix (...) et al.) was column-major and post-multiplication. Most OpenGL-based frameworks follow tradition, though there are some exceptions like OpenTK. Traditional matrix multiplications were done in the following order:
1. Translation
2. Scaling
3. Rotation
But because of the nature of post-multiplying column-major matrices (matrix multiplication is non-commutative) the operations effectively occured from bottom-to-top. Even though you do the multiplication for translation before the one for rotation, rotation is actually applied to the pre-translated coordinates.
In effect, assuming your matrix library follows OpenGL convention, you are doing the sequence of matrix multiplications in reverse.
I'm trying to use OpenCV to do some basic augmented reality. The way I'm going about it is using findChessboardCorners to get a set of points from a camera image. Then, I create a 3D quad along the z = 0 plane and use solvePnP to get a homography between the imaged points and the planar points. From that, I figure I should be able to set up a modelview matrix which will allow me to render a cube with the right pose on top of the image.
The documentation for solvePnP says that it outputs a rotation vector "that (together with [the translation vector] ) brings points from the model coordinate system to the camera coordinate system." I think that's the opposite of what I want; since my quad is on the plane z = 0, I want a a modelview matrix which will transform that quad to the appropriate 3D plane.
I thought that by performing the opposite rotations and translations in the opposite order I could calculate the correct modelview matrix, but that seems not to work. While the rendered object (a cube) does move with the camera image and seems to be roughly correct translationally, the rotation just doesn't work at all; it on multiple axes when it should only be rotating on one, and sometimes in the wrong direction. Here's what I'm doing so far:
std::vector<Point2f> corners;
bool found = findChessboardCorners(*_imageBuffer, cv::Size(5,4), corners,
CV_CALIB_CB_FILTER_QUADS |
CV_CALIB_CB_FAST_CHECK);
if(found)
{
drawChessboardCorners(*_imageBuffer, cv::Size(6, 5), corners, found);
std::vector<double> distortionCoefficients(5); // camera distortion
distortionCoefficients[0] = 0.070969;
distortionCoefficients[1] = 0.777647;
distortionCoefficients[2] = -0.009131;
distortionCoefficients[3] = -0.013867;
distortionCoefficients[4] = -5.141519;
// Since the image was resized, we need to scale the found corner points
float sw = _width / SMALL_WIDTH;
float sh = _height / SMALL_HEIGHT;
std::vector<Point2f> board_verts;
board_verts.push_back(Point2f(corners[0].x * sw, corners[0].y * sh));
board_verts.push_back(Point2f(corners[15].x * sw, corners[15].y * sh));
board_verts.push_back(Point2f(corners[19].x * sw, corners[19].y * sh));
board_verts.push_back(Point2f(corners[4].x * sw, corners[4].y * sh));
Mat boardMat(board_verts);
std::vector<Point3f> square_verts;
square_verts.push_back(Point3f(-1, 1, 0));
square_verts.push_back(Point3f(-1, -1, 0));
square_verts.push_back(Point3f(1, -1, 0));
square_verts.push_back(Point3f(1, 1, 0));
Mat squareMat(square_verts);
// Transform the camera's intrinsic parameters into an OpenGL camera matrix
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
// Camera parameters
double f_x = 786.42938232; // Focal length in x axis
double f_y = 786.42938232; // Focal length in y axis (usually the same?)
double c_x = 217.01358032; // Camera primary point x
double c_y = 311.25384521; // Camera primary point y
cv::Mat cameraMatrix(3,3,CV_32FC1);
cameraMatrix.at<float>(0,0) = f_x;
cameraMatrix.at<float>(0,1) = 0.0;
cameraMatrix.at<float>(0,2) = c_x;
cameraMatrix.at<float>(1,0) = 0.0;
cameraMatrix.at<float>(1,1) = f_y;
cameraMatrix.at<float>(1,2) = c_y;
cameraMatrix.at<float>(2,0) = 0.0;
cameraMatrix.at<float>(2,1) = 0.0;
cameraMatrix.at<float>(2,2) = 1.0;
Mat rvec(3, 1, CV_32F), tvec(3, 1, CV_32F);
solvePnP(squareMat, boardMat, cameraMatrix, distortionCoefficients,
rvec, tvec);
_rv[0] = rvec.at<double>(0, 0);
_rv[1] = rvec.at<double>(1, 0);
_rv[2] = rvec.at<double>(2, 0);
_tv[0] = tvec.at<double>(0, 0);
_tv[1] = tvec.at<double>(1, 0);
_tv[2] = tvec.at<double>(2, 0);
}
Then in the drawing code...
GLKMatrix4 modelViewMatrix = GLKMatrix4MakeTranslation(0.0f, 0.0f, 0.0f);
modelViewMatrix = GLKMatrix4Translate(modelViewMatrix, -tv[1], -tv[0], -tv[2]);
modelViewMatrix = GLKMatrix4Rotate(modelViewMatrix, -rv[0], 1.0f, 0.0f, 0.0f);
modelViewMatrix = GLKMatrix4Rotate(modelViewMatrix, -rv[1], 0.0f, 1.0f, 0.0f);
modelViewMatrix = GLKMatrix4Rotate(modelViewMatrix, -rv[2], 0.0f, 0.0f, 1.0f);
The vertices I'm rendering create a cube of unit length around the origin (i.e. from -0.5 to 0.5 along each edge.) I know with OpenGL translation functions performed transformations in "reverse order," so the above should rotate the cube along the z, y, and then x axes, and then translate it. However, it seems like it's being translated first and then rotated, so perhaps Apple's GLKMatrix4 works differently?
This question seems very similar to mine, and in particular coder9's answer seems like it might be more or less what I'm looking for. However, I tried it and compared the results to my method, and the matrices I arrived at in both cases were the same. I feel like that answer is right, but that I'm missing some crucial detail.
You have to make sure the axis are facing the correct direction. Especially, the y and z axis are facing different directions in OpenGL and OpenCV to ensure the x-y-z basis is direct. You can find some information and code (with an iPad camera) in this blog post.
-- Edit --
Ah ok. Unfortunately, I used these resources to do it the other way round (opengl ---> opencv) to test some algorithms. My main issue was that the row order of the images was inverted between OpenGL and OpenCV (maybe this helps).
When simulating cameras, I came across the same projection matrices that can be found here and in the generalized projection matrix paper. This paper quoted in the comments of the blog post also shows some link between computer vision and OpenGL projections.
I'm not an IOS programmer, so this answer might be misleading!
If the problem is not in the order of applying the rotations and the translation, then suggest using a simpler and more commonly used coordinate system.
The points in the corners vector have the origin (0,0) at the top left corner of the image and the y axis is towards the bottom of the image. Often from math we are used to think of the coordinate system with the origin at the center and y axis towards the top of the image. From the coordinates you're pushing into board_verts I'm guessing you're making the same mistake. If that's the case, it's easy to transform the positions of the corners by something like this:
for (i=0;i<corners.size();i++) {
corners[i].x -= width/2;
corners[i].y = -corners[i].y + height/2;
}
then you call solvePnP(). Debugging this is not that difficult, just print the positions of the four corners and the estimated R and T, and see if they make sense. Then you can proceed to the OpenGL step. Please let me know how it goes.