We want to render a parametrized surface in front of a grid plane and observe the transformation of the grid due to refraction happening at the surface. Our surface is in this simple example a 2D normal distribution which we will view directly from above and the grid plane is placed below:
The surface is given in many triangle directives which we put together in a mesh and used it with
object {
fovea
scale <1,1,3>
texture { pigment {color rgbt <0,0,1,0.5> }}
interior {ior 1.4}
}
The scale here is not necessary and used only to amplify the artifacts. What you see in the image below is, that the refraction seems not to happen smoothly, but creates some sharp artifacts in the underlying grid pattern.
This image was created with Povray 3.6.1 under MacOS X 10.5.6 with the settings +Q9, +A and -J. Can anyone point out a hint? Thanks.
This was a stupid mistake. Since in Mathematica the surface looked really smooth, I assumed that it created a large number of triangle-faces. This assumption was wrong. The rendering engine Mathematica uses, seems to interpolate the normals given for each vertex and therefore the surfaces only looks as it has a high resolution.
A check of the underlying polygons reveals the truth:
Therefore, what looks like refraction artifacts in the rendered image above is actually correct behavior, because the face-normals of neighboring triangles really change that much.
Increasing the resolution of the surface grid solves the problem.
Related
I made a mesh from a Digital Elevation Map that spanned 1x1 degree box of geography, but when I scale the mesh up to 11139m in blender I get these visible jagged shadows on the peaks of the mesh. I'd prefer to not scale everything down but I suppose I can, it just seems like a strange issue I want to better understand.
My goal is to use the landscape in a WebVR application, but when I put this mesh into an Aframe scene it also has this issue. Thanks for any tips!
Quick answer:
I think this may be caused by the clipping start/end values. Also called near/far clipping planes. Adjusting them may fix the issue but also limit the rendering distance.
Longer explanation:
Take a look at this:
It's a simple grayscale, but imagine it is scaled across your entire scene depth (Z depth buffer). The range of this buffer is set by the start/stop clipping (near/far) camera setting.
By default Blender has its start/stop (near/far) clipping set to 0.01 - 1000.
While A-Frame has it like 0.005 - 10000. You may find more information here: A-Frame camera #properties
That means the renderer has to somehow fit every single point in that range somewhere on the grayscale. That may cause overlapping or Z-fighting because it is simply lacking precision to distinguish the details. And that is mainly visible at edges/peaks because the polygons are connected there at acute angles and the program has to round up the Z-values. That causes overlapping visible as darker shadows (most likely the backside of the polygon behind).
You may also want to read more about Z-fighting because it is somewhat related.
Example
I'm working on a fork of Pleasant3D.
When rotating an object being displayed the object always rotates around the same point relative to to itself even if that point is not at the center of the view (e.g. because the user has panned to move the object in the view).
I would like to change this so that the view always rotates the object around the point at the center of the view as it appears to the user instead of the center of the object.
Here is the core of the current code that rotates the object around its center (slightly simplified) (from here):
glLoadIdentity();
// midPlatform is the offset to reach the "middle" of the object (or more specifically the platform on which the object sits) in the x/y dimension.
// This the point around which the view is currently rotated.
Vector3 *midPlatform = [self.currentMachine calcMidBuildPlatform];
glTranslatef((GLfloat)cameraTranslateX - midPlatform.x,
(GLfloat)cameraTranslateY - midPlatform.y,
(GLfloat)cameraOffset);
// trackBallRotation and worldRotation come from trackball.h/c which appears to be
// from an Apple OpenGL sample.
if (trackBallRotation[0] != 0.0f) {
glRotatef (trackBallRotation[0], trackBallRotation[1], trackBallRotation[2], trackBallRotation[3]);
}
// accumlated world rotation via trackball
glRotatef (worldRotation[0], worldRotation[1], worldRotation[2], worldRotation[3]);
glTranslatef(midPlatform.x, midPlatform.y, 0.);
// Now draw object...
What transformations do I need to apply in what order to get the effect I desire?
Some of what I've tried so far
As I understand it this is what the current code does:
"OpenGL performs matrices multiplications in reverse order if multiple transforms are applied to a vertex" (from here). This means that the first transformation to be applied is actually the last one in the code above. It moves the center of the view (0,0) to the center of the object.
This point is then used as the center of rotation for the next two transformations (the rotations).
Finally the midPlatform translation is done in reverse to move the center back to the original location and the XY translations (panning) done by the user is applied. Here also the "camera" is moved away from the object to the proper location (indicated by cameraOffset).
This seems straightforward enough. So what I need to change is instead of translating the center of the view to the center of the object (midPlatform) I need to translate it to the current center of the view as seen by the user, right?
Unfortunately this is where the transformations start affecting each other in interesting ways and I am running into trouble.
I tried changing the code to this:
glLoadIdentity();
glTranslatef(0,
0,
(GLfloat)cameraOffset);
if (trackBallRotation[0] != 0.0f) {
glRotatef (trackBallRotation[0], trackBallRotation[1], trackBallRotation[2], trackBallRotation[3]);
}
// accumlated world rotation via trackball
glRotatef (worldRotation[0], worldRotation[1], worldRotation[2], worldRotation[3]);
glTranslatef(cameraTranslateX, cameraTranslateY, 0.);
In other words, I translate the center of the view to the previous center, rotate around that, and then apply the camera offset to move the camera away to the proper position. This makes the rotation behave exactly the way I want it to, but it introduces a new issue. Now any panning done by the user is relative to the object. For example if the object is rotated so that the camera is looking along the X axis end-on, if the user pans left to right the object appears to be moving closer/further from the user instead of left or right.
I think I can understand why the is (XY camera translations being applied before rotation), and I think what I need to do is figure out a way to cancel out the translation from before the rotation after the rotation (to avoid the weird panning effect) and then to do another translation which translates relative to the viewer (eye coordinate space) instead of the object (object coordinate space) but I'm not sure exactly how to do this.
I found what I think are some clues in the OpenGL FAQ(http://www.opengl.org/resources/faq/technical/transformations.htm), for example:
9.070 How do I transform my objects around a fixed coordinate system rather than the object's local coordinate system?
If you rotate an object around its Y-axis, you'll find that the X- and Z-axes rotate with the object. A subsequent rotation around one of these axes rotates around the newly transformed axis and not the original axis. It's often desirable to perform transformations in a fixed coordinate system rather than the object’s local coordinate system.
The root cause of the problem is that OpenGL matrix operations postmultiply onto the matrix stack, thus causing transformations to occur in object space. To affect screen space transformations, you need to premultiply. OpenGL doesn't provide a mode switch for the order of matrix multiplication, so you need to premultiply by hand. An application might implement this by retrieving the current matrix after each frame. The application multiplies new transformations for the next frame on top of an identity matrix and multiplies the accumulated current transformations (from the last frame) onto those transformations using glMultMatrix().
You need to be aware that retrieving the ModelView matrix once per frame might have a detrimental impact on your application’s performance. However, you need to benchmark this operation, because the performance will vary from one implementation to the next.
And
9.120 How do I find the coordinates of a vertex transformed only by the ModelView matrix?
It's often useful to obtain the eye coordinate space value of a vertex (i.e., the object space vertex transformed by the ModelView matrix). You can obtain this by retrieving the current ModelView matrix and performing simple vector / matrix multiplication.
But I'm not sure how to apply these in my situation.
You need to transform/translate "center of view" point into origin, rotate, then invert that translation, back to the object's transform. This is known as a basis change in linear algebra.
This is way easier to work with if you have a proper 3d-math library (I'm assuming you do have one), and that also helps to to stay far from the deprecated fixed-pipeline APIs. (more on that later).
Here's how I'd do it:
Find the transform for the center of view point in world coordinates (figure it out, then draw it to make sure it's correct, with x,y,z axis too, since the axii are supposed to be correct w.r.t. the view). If you use the center-of-view point and the rotation (usually the inverse of the camera's rotation), this will be a transform from world origin to the view center. Store this in a 4x4 matrix transform.
Apply the inverse of the above transform, so that it becomes the origin. glMultMatrixfv(center_of_view_tf.inverse());
Rotate about this point however you want (glRotate())
Transform everything back to world space (glMultMatrixfv(center_of_view_tf);)
Apply object's own world transform (glTranslate/glRotate or glMultMatrix) and draw it.
About the fixed function pipeline
Back in the old days, there were separate transistors for transforming a vertex (or it's texture coordinates), computing where light was in relation to it applying lights (up to 8) and texturing fragments in many different ways. Simply, glEnable(), enabled fixed blocks of silicon to do some computation in the hardware graphics pipeline. As performance grew, die sized shrunk and people demanded more features, the amount of dedicated silicon grew too, and much of it wasn't used.
Eventually, it got so advanced that you could program it in rather obscene ways (register combiners anyone). And then, it became feasible to actually upload a small assembler program for all vertex-level transforms. Then, it made to sense to keep a lot of silicon there that just did one thing (especially as you could've used those transistors to make the programmable stuff faster), so everything became programmable. If "fixed function" rendering was called for, the driver just converted the state (X lights, texture projections, etc) to shader code and uploaded that as a vertex shader.
So, currently, where even the fragment processing is programmable, there is just a lot of fixed-function options that is used by tons and tons of OpenGL applications, but the silicon on the GPU just runs shaders (and lots of it, in parallell).
...
To make OpenGL more efficient, and the drivers less bulky, and the hardware simpler and useable on mobile/console devices and to take full advantage of the programmable hardware that OpenGL runs on these days, many functions in the API are now marked deprecated. They are not available on OpenGL ES 2.0 and beyond (mobile) and you won't be getting the best performance out of them even on desktop systems (where they will still be in the driver for ages to come, serving equally ancient code bases originating back to the dawn of accelerated 3d graphics)
The fixed-functionness mostly concerns how transforms/lighting/texturing etc. are done by "default" in OpenGL (i.e. glEnable(GL_LIGHTING)), instead of you specifying these ops in your custom shaders.
In the new, programmable, OpenGL, transform matrices are just uniforms in the shader. Any rotate/translate/mult/inverse (like the above) should be done by client code (your code) before being uploaded to OpenGL. (Using only glLoadMatrix is one way to start thinking about it, but instead of using gl_ModelViewProjectionMatrix and the ilk in your shader, use your own uniforms.)
It's a bit of a bother, since you have to implement quite a bit of what was done by the GL driver before, but if you have your own object list/graph with transforms and a transform somewhere etc, it's not that much work. (OTOH, if you have a lot of glTranslate/glRotate in your code, it might be...). As I said, a good 3d-math library is indispensable here.
-..
So, to change the above code to "programmable pipeline" style, you'd just do all these matrix multiplications in your own code (instead of the GL driver doing it, still on the CPU) and then send the resulting matrix to opengl as a uniform before you activate the shaders and draw your object from VBOs.
(Note that modern cards do not have fixed-function code, just a lot of code in the driver to compile fixed-function rendering state to a shader that does the job. No wonder "classic" GL drivers are huge...)
...
Some info about this process is available at Tom's Hardware Guide and probably Google too.
I want to display mesh models in OpenGL ES 2.0, where it clearly shows the actual mesh, so I don't want smooth shading across each primitive/triangle. The only two options I can think about are
Each triangle has its own set of normals, all perpendicular to the triangles surface (but then I guess I can't share vertices among the triangles with this option)
Indicate triangle/primitive edges using black lines and stick to the normal way with shared vertices and one normal for each vertex
Does it have to be like this? Why can't I simply read in primitives and don't specify any normals and somehow let OpenGL ES 2.0 make a flat shade on each face?
Similar question Similar Stackoverflow question, but no suggestion to solution
Because in order to have shading on your mesh (any, smooth or flat), you need a lighting model, and OpenGL ES can't guess it. There is no fixed pipeline in GL ES 2 so you can't use any built-in function that will do the job for you (using a built-in lighting model).
In flat shading, the whole triangle will be drawn with the same color, computed from the angle between its normal and the light source (Yes, you also need a light source, which could simply be the origin of the perspective view). This is why you need at least one normal per triangle.
Then, a GPU works in a very parallelized way, processing several vertices (and then fragments) at the same time. To be efficient, it can't share data among vertices. This is why you need to replicate normals for each vertex.
Also, your mesh can't share vertices among triangles anymore as you said, because they share only the vertex position, not the vertex normal. So you need to put 3 * NbTriangles vertices in you buffer, each one having one position and one normal. You can't either have the benefit of using triangle strips/fans, because none of your faces will have a common vertex with another one (because, again, different normals).
I am trying to develop an iOS app to make any given image (UIImage) warp on selected locations.
So for this task to be accomplished what should be the rightmost way going forward, for now i'm doing some research on doing this on OpenGL (frankly any heads up on the framework would be nice too).
So finally the requirement is to get the UIImage warp on some given locations. (If x, y coordinates are there)
If you're sufficiently familiar with (or willing to learn) OpenGL, then you could do this:
Create a flat, rectangular grid of points to be a mesh that will be displayed with OpenGL.
Apply the image to the mesh as a texture.
When distorting the image at a particular location, you can just decide which points on the mesh will be affected by the distortion, and move them.
You can push points out from the center, or in toward a center, or shift them all in the same direction. If the distortion affects a large area, then you change a lot of points (possibly changing those in the center by more than those near the edges of the affected area).
Not sure what you mean by 'warp'. Do you mean skew it in 3 dimensions? If so you can adjust the CGAffineTransform for the UIImageView you are displaying it in to get that effect.
If you mean some kind of image processing warp, and you are using iOS 5, you can use Core Image for that.
I vaguely remember seeing something in OpenGL (not ES, which was still at v1.0 on the iPhone when I came across this, which is why I never used it) that let me specify which edges of my polygons were considered outlines vs those that made up the interior of faces. As such, this isn't the same as the outline of the entire model (which I know how to do), but rather the outline of a planar face with all its tris basically blended into one poly. For instance, in a cube made up of tri's, each face is actually two tris. I want to render the outline of the square, but not the diagonal across the face. Same thing with a hexagon. That takes four tris, but just one outline for the face.
Now yes, I know I can simply test all the edges to see if they share coplanar faces, but I could have sworn I remember seeing somewhere when you're defining the tri mesh data where you could say 'this line outlines a face whereas this one is inside a face.' That way when rendering, you could set a flag that basically says 'Give me a wireframe, but only the wires around the edges of complete faces, not around the tris that make them up.'
BTW, my target is all platforms that support OpenGL ES 2.0 but my dev platform is iOS. Again, this Im pretty sure was originally in OpenGL and may have been depreciated once shaders came on the scene, but I can't even find a reference to this feature to check if that's the case.
The only way I know now is to have one set of vertices, but two separate sets of indices... one for rendering tris, and another for rendering the wireframes of the faces. It's a real pain since I end up hand-coding a lot of this, which again, I'm 99% sure you can define when rendering the lines.
GL_QUADS, glEdgeFlag and glPolygonMode are not supported in OpenGL ES.
You could use LINES to draw the wireframe: To get hidden lines, first draw black filled triangles (with DEPTH on) and then draw the edges you are interested in with GL_LINES.