Is it possible to create a projection matrix that is horizontally perspective, yet vertically orthographic? I am trying to create a game in Unity (2D) and am just learning about projection matrices. If you look at an engine like Construct 2, it has this capability baked in by default (as you can set parallax based on the x and y axis). Now, I know this can be done with an orthographic camera and scripts to move the backgrounds, but I was wondering if it can be done with a perspective camera.
Thanks!
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I'm building a scene, which I want to view through the orthographic camera, from an angle. I do the following:
Build the scene.
Move the OrbitControl's (camera's) target to the center of the scene.
Move the camera by a certain (unit) vector using spherical coordinates.
Try to adjust the camera's left/right/top/bottom params to keep the object in the view, centered. Also considered adjusting the zoom.
My simplified, ideally positioned scene looks like that:
So I guess it is a problem of a calculation of positions of object extremities after (spherical) transformation and projecting them back into cartesian coordinates. I tried to use Euler transform helper, but it depends on the order of transformation for each of the axis. Quaternions are also non-commutive, and I'm lost. Perhaps I need to calculate how would the widths/heights of the diagonals change after transformation and use these?
A spherical object is photographed from 6 different sides (cube faces). Since the radius and camera distance is known, the z coordinate of every pixel in the images can be calculated.
So I have multiple point clouds (nearly half spheres) of the same physical object as pcl::PointCloud<pcl::PointXYZRGB>.
I know the rough rotational relationship between the models (90 deg rotations), but to stitch them together to a full sphere correctly I need to know the rigid transform more precisely. How can I achieve this? The shapes have no significance in this case, stitching by color matching would be good. But the examples in the documentation all seem to only consider shapes, not colors.
The overlap of the partial models is about 40 degrees.
My question is similar to 3D Scene Panning in perspective projection (OpenGL) except I don't know how to compute the direction in which to move the mesh.
I have a program in which various meshes can be selected. Once a mesh is selected I want it to translate when click-dragging the cursor. When the cursor moves up, I want the mesh to move up, and so on for the appropriate direction. In other words, I want the mesh to translate in directions along the plane that is perpendicular to the viewing direction.
I have the Vector2 for the Delta (x,y) in cursor postion, and I have the Vector3 viewDirection of the camera and the center of the mesh. How can I figure out which way to translate the mesh in 3d space with the Delta and viewDirection? Will I need other information in order to to this calculation (such as the up, or eye)?
It doesn't matter if if the scale of the translation is off, I'm just trying to figure out the direction right now.
EDIT: for some reason I had a confusion about getting the up direction. Clearly it can be calculated by applying the camera rotation to the specified perspective up vector.
You'll need an additional vector, upDirection, which is the unit vector pointing "up" from your camera. You can now cross-product viewDirection and upDirection to get rightDirection, the vector pointing "right" from your camera.
You want to map y deltas to motion along upDirection (or -upDirection) and x deltas to motion in rightDirection. These vectors are in world-space.
You may want to scale the translation speed to match the mouse speed. If you are using perspective projection you'll want to scale the translation speed with your model's depth with respect to your camera (The further the object is from your camera, the faster you will need to move it if you want it to match the mouse.)
I want to project a grid on the xz-plane like shown here:
To do that, I created a vertex grid with x and z range [-1|1]. In the shader I multiply the xz screen coordinate of a vertex with the inverse of the View-Projection matrix. Then I want to adjust the height, depending on the new world xz coordinates and finally I transform these coordinates back to screenspace by multiplying them with the View-Projection matrix.
I dont know why, but I get a very strange plane shown on the screen. Are the mathematical oprations I use correct?
The grid that you initially create, is that in projection space or actual screen co-ords? It sounds like it is in projection space since you only transform it with the inverse of the view-projection matrix to get into world co-ords. I think you need to include the "Window" matrix too i.e. transform them by the inverse of the View-Projection-Window matrix (and similarly on the way back to screen co-ords).
Edit:
I'm probably not understanding exactly what it is you're trying to do so here's some questions back. :)
Are you trying to take the grid that's shown in the screenshot in your question and project that onto world z-x co-ordinates? If so, then why do you start with a grid of z-x values? Also, if you apply an inverse view matrix to those then surely you would end up with a line since the camera looks along z although your second screenshots show that you are getting a plane. I'm a bit confused.
I'm making a side scroller similar to Castle Crashers and right now I'm using SAT for collision detection. That works great, but I want to simulate level "depth" by allowing objects to move up and down on the screen, basically along a z-axis (like this screenshot http://favoniangamers.files.wordpress.com/2009/07/castle-crashers-ps3.jpg). This isn't an isometric game, but rather uses parallax scrolling.
I added a z component to my vector class, and I plan to cull collisions based on the 'thickness' of a shape and it's z position. I'm just not sure how calculate the positions of shapes for rendering or how to add jumping with gravity. How do I calculate the max y value (for the ground) as the z position changes? Basically it's the relationship of the z and y axis that confuses me.
I'd appreciate links to resources if anyone knows of this topic.
Thanks!
It's actually possible to make your collision detection algorithm dimensionally agnostic. Just have a collision detector that works along one dimension, use that to check each dimension, and your answer to "are these colliding or not" is the logical AND of the collision detection along each of the dimensions.
Your game should be organised to keep the interaction of game objects, and the rendering of the game to the screen completely seperate. You can think of these two sections of the program as the "model" and the "view". In the model, you have a full 3D world, with 3 axes. You can't go halvesies on this point without some level of pain. Your model must be proper 3D.
The view will read the location of all the game objects, and project them onto the screen using the camera definition. For this part you don't need a full 3D rendering engine. The correct technical term for the perspective you're talking about is "oblique", and it can be seen in many ancient chinese and japanese scroll paintings and prints- in particular look for images of "The Tale of Genji".
The on screen position of an object (including the ground surface!) goes something like this:
DEPTH_RATIO=0.5;
view_x=model_x-model_z*DEPTH_RATIO-camera_x;
view_y=model_y+model_z*DEPTH_RATIO-camera_y;
you can modify for a straight orthographic front projection:
DEPTH_RATIO=0.5;
view_x=model_x-camera_x;
view_y=model_y+model_z*DEPTH_RATIO-camera_y;
And of course don't forget to cull objects outside the volume defined by the camera.
You can also use this mechanism to handle the positioning of parallax layers for you. This is of course, a matter changing your camera to a 1-point perspective projection instead of an orthographic projection. You don't have to use this to change the rendered size of your sprites, but it will help you manage the x position of objects realistically. if you're up for a challenge, you could even mix projections- use 1 point perspective for deep backgrounds, and the orthographic stuff for the foreground.
You should separate your conceptual Y axis used by you physics calculation (collision detection etc.) and the Y axis you actually draw on the screen. That way it becomes less confusing.
Just do calculations per normal pretending there is no relationship between Y and Z axis then when you actually draw the object on the screen you simulate the Z axis using the Y axis:
screen_Y = Y + Z/some_fudge_factor;
Actually, this is how real 3d engines work. After all the world calculations are done the X, Y and Z coordinates are mapped onto screen_X and screen_Y via a function (usually a bit more complicated than the equation above, but just a bit).
For example, to implement pseudo-isormetric view in your game you can even apply Z to the screen_X axis so objects are displaced diagonally instead of vertically.