I have the following issue when trying to map UV-coordinates to a sphere
Here is the code I'm using to get my UV-coordinates
glm::vec2 calcUV( glm::vec3 p)
{
p = glm::normalize(p);
const float PI = 3.1415926f;
float u = ((glm::atan(p.x, p.z) / PI) + 1.0f) * 0.5f;
float v = (asin(p.y) / PI) + 0.5f;
return glm::vec2(u, v);
}
The issue was very well explained at this stackoverflow question, although, I still don't get how can I fix it. From what I've been reading, I have to create a duplicate pair of vertices. Does anyone know some good and effcient way of doing it ?
The problem you have is, that at the seam your texture coordinates "roll" back to 0, so you get the whole texture mapped, mirrored onto the seam. To avoid this you should use GL_WRAP repeat mode and at the seam finish with vertices with texture coordinates >= 1 (don't roll back to 0). Remember that a vertex consists of the whole tuple of all its attributes and vertices with different attribute values are different in the whole, so there's no point in trying to "share" the vertices.
Another way to do it is simply to pass the object coordinates of the sphere into the pixel shader, and calculate the UV in "perfect" spherical space.
Be aware that you will need to pass the local derivatives so that you don't merely reduce your seam from several pixels to one.
Otherwise, yes. You need to duplicate vertices along the same edge as u=0, and likewise repeat the vertices at the poles. In this way, your object topology will become a rectangle: just like your texture.
Related
A quick summary:
I've a simple Quad tree based terrain rendering system that builds terrain patches which then sample a heightmap in the vertex shader to determine the height of each vertex.
The exact same calculation is done on the CPU for object placement and co.
Super straightforward, but now after adding some systems to procedurally place objects I've discovered that they seem to be misplaced by just a small amount. To debug this I render a few crosses as single models over the terrain. The crosses (red, green, blue lines) represent the height read from the CPU. While the terrain mesh uses a shader to translate the vertices.
(I've also added a simple odd/even gap over each height value to rule out a simple offset issue. So those ugly cliffs are expected, the submerged crosses are the issue)
I'm explicitly using GL_NEAREST to be able to display the "raw" height value:
As you can see the crosses are sometimes submerged under the terrain instead of representing its exact height.
The heightmap is just a simple array of floats on the CPU and on the GPU.
How the data is stored
A simple vector<float> which is uploaded into a GL_RGB32F GL_FLOAT buffer. The floats are not normalized and my terrain usually contains values between -100 and 500.
How is the data accessed in the shader
I've tried a few things to rule out errors, the inital:
vec2 terrain_heightmap_uv(vec2 position, Heightmap heightmap)
{
return (position + heightmap.world_offset) / heightmap.size;
}
float terrain_read_height(vec2 position, Heightmap heightmap)
{
return textureLod(heightmap.heightmap, terrain_heightmap_uv(position, heightmap), 0).r;
}
Basics of the vertex shader (the full shader code is very long, so I've extracted the part that actually reads the height):
void main()
{
vec4 world_position = a_model * vec4(a_position, 1.0);
vec4 final_position = world_position;
// snap vertex to grid
final_position.x = floor(world_position.x / a_quad_grid) * a_quad_grid;
final_position.z = floor(world_position.z / a_quad_grid) * a_quad_grid;
final_position.y = terrain_read_height(final_position.xz, heightmap);
gl_Position = projection * view * final_position;
}
To ensure the slightly different way the position is determined I tested it using hardcoded values that are identical to how C++ reads the height:
return texelFetch(heightmap.heightmap, ivec2((position / 8) + vec2(1024, 1024)), 0).r;
Which gives the exact same result...
How is the data accessed in the application
In C++ the height is read like this:
inline float get_local_height_safe(uint32_t x, uint32_t y)
{
// this macro simply clips x and y to the heightmap bounds
// it does not interfer with the result
BB_TERRAIN_HEIGHTMAP_BOUND_XY_TO_SAFE;
uint32_t i = (y * _size1d) + x;
return buffer->data[i];
}
inline float get_height_raw(glm::vec2 position)
{
position = position + world_offset;
uint32_t x = static_cast<int>(position.x);
uint32_t y = static_cast<int>(position.y);
return get_local_height_safe(x, y);
}
float BB::Terrain::get_height(const glm::vec3 position)
{
return heightmap->get_height_raw({position.x / heightmap_unit_scale, position.z / heightmap_unit_scale});
}
What have I tried:
Comparing the Buffers
I've dumped the first few hundred values from the vector. And compared it with the floating point buffer uploaded to the GPU using Nvidia Nsight, they are equal, rounding/precision errors there.
Sampling method
I've tried texture, textureLod and texelFetch to rule out some issue there, they all give me the same result.
Rounding
The super strange thing, when I round all the height values. They are perfectly aligned which just screams floating point precision issues.
Position snapping
I've tried rounding, flooring and ceiling the position, to ensure the position always maps to the same texel. I also tried adding an epsilon offset to rule out a positional precision error (probably stupid because the terrain is stable...)
Heightmap sizes
I've tried various heightmaps, also of different sizes.
Heightmap patterns
I've created a heightmap containing a pattern to ensure the position is not just offsetet.
I'm just wondering if there was any way which one can perform mouse picking detection onto any object. Whether it would be generated object or imported object.
[Idea] -
The idea I have in mind is that, there would be iterations with every object in the scene. Checking if the mouse ray has intersected with an object. For checking the intersection, it would check the mouse picking ray with the triangles that make up the object.
[Pros] -
I believe the benefit of this approach is that, every object can be detected with mouse picking since they all inherit from the detection method.
[Cons] -
I believe this drawbacks are mainly the speed and the method being very expensive. So would need fine tuning of optimization.
[Situation] -
In the past I have read about mouse picking and I too have implemented some basic form of mouse picking. But all those were crappy work which I am not proud of. So again today, I have re-read some of the stuff from online. Nowadays I see alot of mouse picking using color ids and shaders. I'm not too keen for this method. I'm more into a mathematical side.
So here is my mouse picking ray thingamajig.
maths::Vector3 Camera::Raycast(s32 mouse_x, s32 mouse_y)
{
// Normalized Device Coordinates
maths::Vector2 window_size = Application::GetApplication().GetWindowSize();
float x = (2.0f * mouse_x) / window_size.x - 1.0f;
float y = 1.0f;
float z = 1.0f;
maths::Vector3 normalized_device_coordinates_ray = maths::Vector3(x, y, z);
// Homogeneous Clip Coordinates
maths::Vector4 homogeneous_clip_coordinates_ray = maths::Vector4(normalized_device_coordinates_ray.x, normalized_device_coordinates_ray.y, -1.0f, 1.0f);
// 4D Eye (Camera) Coordinates
maths::Vector4 camera_ray = maths::Matrix4x4::Invert(projection_matrix_) * homogeneous_clip_coordinates_ray;
camera_ray = maths::Vector4(camera_ray.x, camera_ray.y, -1.0f, 0.0f);
// 4D World Coordinates
maths::Vector3 world_coordinates_ray = maths::Matrix4x4::Invert(view_matrix_) * camera_ray;
world_coordinates_ray = world_coordinates_ray.Normalize();
return world_coordinates_ray;
}
I have this ray plane intersection function which calculates if a certain ray as intersected with a certain plane. DUH!
Here is the code for that.
bool Camera::RayPlaneIntersection(const maths::Vector3& ray_origin, const maths::Vector3& ray_direction, const maths::Vector3& plane_origin, const maths::Vector3& plane_normal, float& distance)
{
float denominator = plane_normal.Dot(ray_direction);
if (denominator >= 1e-6) // 1e-6 = 0.000001
{
maths::Vector3 vector_subtraction = plane_origin - ray_origin;
distance = vector_subtraction.Dot(plane_normal);
return (distance >= 0);
}
return false;
}
There are many more out there. E.g. Plane Sphere Intersection, Plane Disk Intersection. These things are like very specific. So it feel that is very hard to do mouse picking intersections on a global scale. I feel this way because, for this very RayPlaneIntersection function. What I expect to do with it is, retrieve the objects in the scene and retrieve all the normals for that object (which is a pain in the ass). So now to re-emphasize my question.
Is there already a method out there which I don't know, that does mouse picking in one way for all objects? Or am I just being stupid and not knowing what to do when I have everything?
Thank you. Thank you.
Yes, it is possible to do mouse-picking with OpenGL: you render all the geometry into a special buffer that stores a unique id of the object instead of its shaded color, then you just look at what value you got at the pixel below the mouse and know the object by its id that is written there. However, although it might be simpler, it is not a particularly efficient solution if your camera or geometry constantly moves.
Instead, doing an analytical ray-object intersection is the way to go. However, you don't need to check the intersection of every triangle of every object against the ray. That would be inefficient indeed. You should cull entire objects by their bounding boxes, or even portions of the whole scene. Game engines have their own spacial index data structure to speed-up ray-object intersections. They need it not only for mouse picking, but also for collision-detection, physics simulations, AI, and what-not.
Also note that the geometry used for the picking might be different from the one used for rendering. One example that comes to mind is that of semi-transparent objects.
I am tracking a ball using the rgb data from kinect. After this I look up the corresponding depth data. Both of this is working splendid. Now I want to have the actual x,y,z world coordinates (i.e skeleton Space) instead of the x_screen, y_screen and depth values. Unfortunately the methods given by the kinect sdk (http://msdn.microsoft.com/en-us/library/hh973078.aspx) don`t help me. Basically i need a function "NuiImageGetSkeletonCoordinatesFromColorPixel" but i does not exist. All the functions basically go in the opposite direction
I know this can probably be done with openNI but i can not use it for other reasons.
Is there a function that does this for me or do i have to do the conversion myself? If I have to do it myself, how would i do this? I sketched up a little diagram http://i.imgur.com/ROBJW8Q.png - do you think this would work?
Check the CameraIntrinsics.
typedef struct _CameraIntrinsics
{
float FocalLengthX;
float FocalLengthY;
float PrincipalPointX;
float PrincipalPointY;
float RadialDistortionSecondOrder;
float RadialDistortionFourthOrder;
float RadialDistortionSixthOrder;
} CameraIntrinsics;
You can get it from ICoordinateMapper::GetDepthCameraIntrinsics.
Then, for every pixel (u,v,d) in depth space, you can get the coordinate in world space by doing this:
x = (u - principalPointX) / focalLengthX * d;
y = (v - principalPointY) / focalLengthY * d;
z = d;
For color space pixel, you need to first find its associated depth space pixel, which you should use ICoordinateMapper::MapCameraPointTodepthSpace. Since not all color pixel has its associated depth pixel (1920x1080 vs 512x424), you can't have the full-HD color point cloud.
I had some fun making my first shaders and my first test subject was a 100x100 quad faced picture.
I thought I would learn how to use TRIANGLE_STRIP so I switched it, moved one of the vertex calls so it would look square again. Turned my shader on and there was a duplicate right behind it of only one face but it had the entire texture on it. I have only one set of draw calls for this shape....
Heres my shape code:
glBegin(GL_TRIANGLE_STRIP);
float vx;
float vy;
for(float x=0; x<100; x++){
for(float y=0; y<100; y++){
float vx=x/5.0;
float vy=y/5.0;
glTexCoord2f(0.01*x, 0.01*y);
glVertex3f(vx, vy, 0);
glTexCoord2f(0.01+0.01*x, 0.01*y);
glVertex3f(.2+vx, vy, 0);
glTexCoord2f(0.01*x, 0.01+0.01*y);
glVertex3f(vx, .2+vy, 0);
glTexCoord2f(0.01+0.01*x, 0.01+0.01*y);
glVertex3f(.2+vx, .2+vy, 0);
}}
glEnd();
And my (vertex) shader code:
uniform float uTime,uWaveintensity,uWavespeed;
uniform float uZwave1,uZwave2,uXwave,uYwave;
void main(){
vec4 position = gl_Vertex;
gl_TexCoord[0] = gl_MultiTexCoord0;
position.z=((sin(position.x+uTime*uWavespeed)*uZwave1)+(sin(position.y+uTime*uWavespeed))*uZwave2)*uWaveintensity;
position.x=position.x+(sin(position.x+uTime*uWavespeed)*uXwave)*uWaveintensity;
position.y=position.y+(sin(position.y+uTime*uWavespeed)*uYwave)*uWaveintensity;
gl_Position = gl_ModelViewProjectionMatrix * position;
}
If anyone has any info on drawing more efficiently with shared vertices(triangle_strips) I've googled but I don't understand any so far XD. I wanna know.
screenshot(s):
with 8x8 faces
same thing same angle,lines=ghost
I see whats happening now, but I don't know how to fix it.
I don't think you can create a 100x100 quad plane with triangle strips this way. Now you're going by rows and columns just in one direction, which means that the last 2 vertices of first row will create a triangle with the first vertex of the second row and that's not what you want.
I'd suggest you to start with 2x2 pattern just to learn how triangle strips work, then move to 3x3 and 4x4 to see what is a difference between odd and even situations. When you have some understanding of the problems you can create universal algorithm and change your size to 100.
After this all you can focus on the vertex shader to make it waving.
And for the future: never start from big data if you're learning how the things work. :)
EDIT:
Since I wrote this answer I learned that you already CAN make two dimmensional grid with one tri-strip, using degenerate triangles :).
When a triangle uses the same vertex twice it will be ignored by the rasterizer during rendering, so at the end of your first strip you can create a degenerate triangle using last vertex of first strip and first vertex of the second strip. It doesn't matter which of the two vertexes you'll use as the 3rd one, as long as they are in the correct order (e.g. 1,1,2 or 1,2,2). This way you've created a triangle that won't be drawn, but it will move the next 'starting' point to beginning of your 2nd strip, where you can continue building your mesh.
The drawback is that you create some triangles, that will be transformed but not drawn (there will be not many of them), but the advantage is that you run just one 'draw strip' command to GPU which is much faster.
I am developing a small tool for 3D visualization of molecules.
For my project i choose to make a thing in the way of what Mr "Brad Larson" did with his Apple software "Molecules". A link where you can find a small presentation of the technique used : Brad Larsson software presentation
For doing my job i must compute sphere impostor and cylinder impostor.
For the moment I have succeed to do the "Sphere Impostor" with the help of another tutorial Lies and Impostors
for summarize the computing of the sphere impostor : first we send a "sphere position" and the "sphere radius" to the "vertex shader" which will create in the camera-space an square which always face the camera, after that we send our square to the fragment shader where we use a simple ray tracing to find which fragment of the square is included in the sphere, and finally we compute the normal and the position of the fragment to compute lighting. (another thing we also write the gl_fragdepth for giving a good depth to our impostor sphere !)
But now i am blocked in the computing of the cylinder impostor, i try to do a parallel between the sphere impostor and the cylinder impostor but i don't find anything, my problem is that for the sphere it was some easy because the sphere is always the same no matter how we see it, we will always see the same thing : "a circle" and another thing is that the sphere was perfectly defined by Math then we can find easily the position and the normal for computing lighting and create our impostor.
For the cylinder it's not the same thing, and i failed to find a hint to modeling a form which can be used as "cylinder impostor", because the cylinder shows many different forms depending on the angle we see it !
so my request is to ask you about a solution or an indication for my problem of "cylinder impostor".
In addition to pygabriels answer I want to share a standalone implementation using the mentioned shader code from Blaine Bell (PyMOL, Schrödinger, Inc.).
The approach, explained by pygabriel, also can be improved. The bounding box can be aligned in such a way, that it always faces to the viewer. Only two faces are visible at most. Hence, only 6 vertices (ie. two faces made up of 4 triangles) are needed.
See picture here, the box (its direction vector) always faces to the viewer:
Image: Aligned bounding box
For source code, download: cylinder impostor source code
The code does not cover round caps and orthographic projections. It uses geometry shader for vertex generation. You can use the shader code under the PyMOL license agreement.
I know this question is more than one-year old, but I'd still like to give my 2 cents.
I was able to produce cylinder impostors with another technique, I took inspiration from pymol's code. Here's the basic strategy:
1) You want to draw a bounding box (a cuboid) for the cylinder. To do that you need 6 faces, that translates in 18 triangles that translates in 36 triangle vertices. Assuming that you don't have access to geometry shaders, you pass to a vertex shader 36 times the starting point of the cylinder, 36 times the direction of the cylinder, and for each of those vertex you pass the corresponding point of the bounding box. For example a vertex associated with point (0, 0, 0) means that it will be transformed in the lower-left-back corner of the bounding box, (1,1,1) means the diagonally opposite point etc..
2) In the vertex shader, you can construct the points of the cylinder, by displacing each vertex (you passed 36 equal vertices) according to the corresponding points you passed in.
At the end of this step you should have a bounding box for the cylinder.
3) Here you have to reconstruct the points on the visible surface of the bounding box. From the point you obtain, you have to perform a ray-cylinder intersection.
4) From the intersection point you can reconstruct the depth and the normal. You also have to discard intersection points that are found outside of the bounding box (this can happen when you view the cylinder along its axis, the intersection point will go infinitely far).
By the way it's a very hard task, if somebody is interested here's the source code:
https://github.com/chemlab/chemlab/blob/master/chemlab/graphics/renderers/shaders/cylinderimp.frag
https://github.com/chemlab/chemlab/blob/master/chemlab/graphics/renderers/shaders/cylinderimp.vert
A cylinder impostor can actually be done just the same way as a sphere, like Nicol Bolas did it in his tutorial. You can make a square facing the camera and colour it that it will look like a cylinder, just the same way as Nicol did it for spheres. And it's not that hard.
The way it is done is ray-tracing of course. Notice that a cylinder facing upwards in camera space is kinda easy to implement. For example intersection with the side can be projected to the xz plain, it's a 2D problem of a line intersecting with a circle. Getting the top and bottom isn't harder either, the z coordinate of the intersection is given, so you actually know the intersection point of the ray and the circle's plain, all you have to do is to check if its inside the circle. And basically, that's it, you get two points, and return the closer one (the normals are pretty trivial too).
And when it comes to an arbitrary axis, it turns out to be almost the same problem. When you solve equations at the fixed axis cylinder, you are solving them for a parameter that describes how long do you have to go from a given point in a given direction to reach the cylinder. From the "definition" of it, you should notice that this parameter doesn't change if you rotate the world. So you can rotate the arbitrary axis to become the y axis, solve the problem in a space where equations are easier, get the parameter for the line equation in that space, but return the result in camera space.
You can download the shaderfiles from here. Just an image of it in action:
The code where the magic happens (It's only long 'cos it's full of comments, but the code itself is max 50 lines):
void CylinderImpostor(out vec3 cameraPos, out vec3 cameraNormal)
{
// First get the camera space direction of the ray.
vec3 cameraPlanePos = vec3(mapping * max(cylRadius, cylHeight), 0.0) + cameraCylCenter;
vec3 cameraRayDirection = normalize(cameraPlanePos);
// Now transform data into Cylinder space wherethe cyl's symetry axis is up.
vec3 cylCenter = cameraToCylinder * cameraCylCenter;
vec3 rayDirection = normalize(cameraToCylinder * cameraPlanePos);
// We will have to return the one from the intersection of the ray and circles,
// and the ray and the side, that is closer to the camera. For that, we need to
// store the results of the computations.
vec3 circlePos, sidePos;
vec3 circleNormal, sideNormal;
bool circleIntersection = false, sideIntersection = false;
// First check if the ray intersects with the top or bottom circle
// Note that if the ray is parallel with the circles then we
// definitely won't get any intersection (but we would divide with 0).
if(rayDirection.y != 0.0){
// What we know here is that the distance of the point's y coord
// and the cylCenter is cylHeight, and the distance from the
// y axis is less than cylRadius. So we have to find a point
// which is on the line, and match these conditions.
// The equation for the y axis distances:
// rayDirection.y * t - cylCenter.y = +- cylHeight
// So t = (+-cylHeight + cylCenter.y) / rayDirection.y
// About selecting the one we need:
// - Both has to be positive, or no intersection is visible.
// - If both are positive, we need the smaller one.
float topT = (+cylHeight + cylCenter.y) / rayDirection.y;
float bottomT = (-cylHeight + cylCenter.y) / rayDirection.y;
if(topT > 0.0 && bottomT > 0.0){
float t = min(topT,bottomT);
// Now check for the x and z axis:
// If the intersection is inside the circle (so the distance on the xz plain of the point,
// and the center of circle is less than the radius), then its a point of the cylinder.
// But we can't yet return because we might get a point from the the cylinder side
// intersection that is closer to the camera.
vec3 intersection = rayDirection * t;
if( length(intersection.xz - cylCenter.xz) <= cylRadius ) {
// The value we will (optianally) return is in camera space.
circlePos = cameraRayDirection * t;
// This one is ugly, but i didn't have better idea.
circleNormal = length(circlePos - cameraCylCenter) <
length((circlePos - cameraCylCenter) + cylAxis) ? cylAxis : -cylAxis;
circleIntersection = true;
}
}
}
// Find the intersection of the ray and the cylinder's side
// The distance of the point and the y axis is sqrt(x^2 + z^2), which has to be equal to cylradius
// (rayDirection.x*t - cylCenter.x)^2 + (rayDirection.z*t - cylCenter.z)^2 = cylRadius^2
// So its a quadratic for t (A*t^2 + B*t + C = 0) where:
// A = rayDirection.x^2 + rayDirection.z^2 - if this is 0, we won't get any intersection
// B = -2*rayDirection.x*cylCenter.x - 2*rayDirection.z*cylCenter.z
// C = cylCenter.x^2 + cylCenter.z^2 - cylRadius^2
// It will give two results, we need the smaller one
float A = rayDirection.x*rayDirection.x + rayDirection.z*rayDirection.z;
if(A != 0.0) {
float B = -2*(rayDirection.x*cylCenter.x + rayDirection.z*cylCenter.z);
float C = cylCenter.x*cylCenter.x + cylCenter.z*cylCenter.z - cylRadius*cylRadius;
float det = (B * B) - (4 * A * C);
if(det >= 0.0){
float sqrtDet = sqrt(det);
float posT = (-B + sqrtDet)/(2*A);
float negT = (-B - sqrtDet)/(2*A);
float IntersectionT = min(posT, negT);
vec3 Intersect = rayDirection * IntersectionT;
if(abs(Intersect.y - cylCenter.y) < cylHeight){
// Again it's in camera space
sidePos = cameraRayDirection * IntersectionT;
sideNormal = normalize(sidePos - cameraCylCenter);
sideIntersection = true;
}
}
}
// Now get the results together:
if(sideIntersection && circleIntersection){
bool circle = length(circlePos) < length(sidePos);
cameraPos = circle ? circlePos : sidePos;
cameraNormal = circle ? circleNormal : sideNormal;
} else if(sideIntersection){
cameraPos = sidePos;
cameraNormal = sideNormal;
} else if(circleIntersection){
cameraPos = circlePos;
cameraNormal = circleNormal;
} else
discard;
}
From what I can understand of the paper, I would interpret it as follows.
An impostor cylinder, viewed from any angle has the following characteristics.
From the top, it is a circle. So considering you'll never need to view a cylinder top down, you don't need to render anything.
From the side, it is a rectangle. The pixel shader only needs to compute illumination as normal.
From any other angle, it is a rectangle (the same one computed in step 2) that curves. Its curvature can be modeled inside the pixel shader as the curvature of the top ellipse. This curvature can be considered as simply an offset of each "column" in texture space, depending on viewing angle. The minor axis of this ellipse can be computed by multiplying the major axis (thickness of the cylinder) with a factor of the current viewing angle (angle / 90), assuming that 0 means you're viewing the cylinder side-on.
Viewing angles. I have only taken the 0-90 case into account in the math below, but the other cases are trivially different.
Given the viewing angle (phi) and the diameter of the cylinder (a) here's how the shader needs to warp the Y-Axis in texture space Y = b' sin(phi). And b' = a * (phi / 90). The cases phi = 0 and phi = 90 should never be rendered.
Of course, I haven't taken the length of this cylinder into account - which would depend on your particular projection and is not an image-space problem.