I have been wondering for a while about how the transform matrix in spriteBatch is implemented. I've created a 2D camera, and the transform matrix is as follows:
if (needUpdate)
transformMatrix =
Matrix.CreateTranslation(-Position.X, -Position.Y, 0) *
Matrix.CreateScale(curZoom, curZoom, 1) ; needUpdate = false;
The camera works as good as I want, but I just want to know how the transformation is applied: Does the transformation only affects the axis of the sprites, or the screen co-ordinates too?
Thanks in advance!
I see you've answered your own question, but to provide complete information - SpriteBatch provides a similar interface to the traditional world-view-projection system of transformations.
The SpriteBatch class has an implicit projection matrix that takes coordinates in the "client space" of the viewport ((0,0) at the top left, one unit per pixel) and puts them on screen.
The Begin call has an overload that accepts a transformation matrix, which is the equivalent of a view matrix used for moving the camera around.
And the Draw call, while not actually using a matrix, allows you to specify position, rotation, scale, etc - equivalent to a world matrix used for positioning a model in the scene (model space to world space).
So you start with your "model" equivalent - which for SpriteBatch is a quad (sprite) of the size of the texture (or source rectangle). When drawn, that quad is transformed to its world coordinates, then that is transformed to its view coordinates, and then finally that is transformed to its projection coordinates.
Related
I use DirectX Toolkit to display a 3d model, following the 'Rendering the model' and my pyramid is displayed:
When trying to transform the object, the scaling and rotation work well but I'm not sure how to move the object (translate) around. Basically I'm looking for an algorithm that determines, given the current camera position, focus, viewport and the rendered model (which the DirectX toolkit gives me the bounding box so it's "size") the minimum and maximum values for XYZ translation so the object remains visible.
The bounding box is always the same, no matter the view port size, so how do I compare it's size against my viewport?
Please excuse my newbiness, I'm not a 3D developer, at least yet.
The "Simple Rendering" example which draws a triangle:
Matrix proj = Matrix::CreateScale( 2.f/float(backBufferWidth),
-2.f/float(backBufferHeight), 1.f)
* Matrix::CreateTranslation( -1.f, 1.f, 0.f );
m_effect->SetProjection(proj);
says that the normalized triangle size is [1,1,1] but here normalized values do not work.
TL:DR: To move your model around the world, create a matrix for the translation and set it as the world matrix with SetWorld.
Matrix world = Matrix::CreateTranslation( 2.f, 1.f, 3.f);
m_effect->SetWorld(world);
// Also be sure you have called SetView and SetProjection for the 3D camera setup
//covered in the 3D shapes / Rendering a model tutorial
You should start with a basic review of 3D transformations, in particular the world -> view -> projection transformation pipeline.
The world transformation performs the affine transformation to get the model you are rendering into it's 'world' position. (a.k.a. 'local coordinates to world coordinates transformation').
The view transformation performs the transformation to get world positions into the camera's point of view (i.e. position and direction) (a.k.a. 'world coordinates to view coordinates transformation').
The projection transformation performs the transformation to get the view positions into the canonical "-1 to 1" range that the actual hardware uses, including any perspective projection (a.k.a. 'view coordinates to 'clip' coordinates transformation).
The hardware itself performs the final step of converting the "-1 to 1" to pixel locations in the render target based on the Direct3D SetViewport information (a.k.a. 'clip' coordinates to pixel coordinates transformation).
This Direct3D 9 era article is a bit dated, but it covers the overall idea well.
In the DirectX Tool Kit BasicEffect system, there are distinct methods for each of these matrices: SetWorld, SetView, and SetProjection. There is also a helper if you want to set all three at once SetMatrices.
The simple rendering tutorial is concerned with the simplest form of rendering, 2D rendering, where you want the coordinates you provide to be in natural 'pixel coordinates'
Matrix proj = Matrix::CreateScale( 2.f/float(backBufferWidth),
-2.f/float(backBufferHeight), 1.f)
* Matrix::CreateTranslation( -1.f, 1.f, 0.f );
m_effect->SetProjection(proj);
The purpose of this matrix is to basically 'undo' what the SetViewport will do so that you can think in simple pixel coordinates. It's not suitable for 3D models.
In the 3D shapes tutorial I cover the basic camera model, but I leave the world matrix as the identity so the shape is sitting at the world origin.
m_view = Matrix::CreateLookAt(Vector3(2.f, 2.f, 2.f),
Vector3::Zero, Vector3::UnitY);
m_proj = Matrix::CreatePerspectiveFieldOfView(XM_PI / 4.f,
float(backBufferWidth) / float(backBufferHeight), 0.1f, 10.f);
In the Rendering a model tutorial, I also leave the world matrix as identity. I get into the basics of this in Basic game math tutorial.
One of the nice properties of affine transformations is that you can perform them all at once by transforming by the concatenation of the individual transforms. Point p transformed by matrix W, then transformed by matrix V, then transformed by matrix P is the same as point p transformed by matrix W * V * P.
I want to create the same transforming effect on XNA 4 as Photoshop does:
Transform tool is used to scale, rotate, skew, and just distort the perspective of any graphic you’re working with in general
This is what all the things i want to do in XNA with any textures http://www.tutorial9.net/tutorials/photoshop-tutorials/using-transform-in-photoshop/
Skew: Skew transformations slant objects either vertically or horizontally.
Distort: Distort transformations allow you to stretch an image in ANY direction freely.
Perspective: The Perspective transformation allows you to add perspective to an object.
Warping an Object(Im interesting the most).
Hope you can help me with some tutorial or somwthing already made :D, iam think vertex has the solution but maybe.
Thanks.
Probably the easiest way to do this in XNA is to pass a Matrix to SpriteBatch.Begin. This is the overload you want to use: MSDN (the transformMatrix argument).
You can also do this with raw vertices, with an effect like BasicEffect by setting its World matrix. Or by setting vertex positions manually, perhaps transforming them with Vector3.Transform().
Most of the transformation matrices you want are provided by the Matrix.Create*() methods (MSDN). For example, CreateScale and CreateRotationZ.
There is no provided method for creating a skew matrix. It should be something like this:
Matrix skew = Matrix.Identity;
skew.M12 = (float)Math.Tan(MathHelper.ToRadians(36.87f));
(That is to skew by 36.87f degrees, which I pulled off this old answer of mine. You should be able to find the full maths for a skew matrix via Google.)
Remember that transformations happen around the origin of world space (0,0). If you want to, for example, scale around the centre of your sprite, you need to translate that sprite's centre to the origin, apply a scale, and then translate it back again. You can combine matrix transforms by multiplying them. This example (untested) will scale a 200x200 image around its centre:
Matrix myMatrix = Matrix.CreateTranslation(-100, -100, 0)
* Matrix.CreateScale(2f, 0.5f, 1f)
* Matrix.CreateTranslation(100, 100, 0);
Note: avoid scaling the Z axis to 0, even in 2D.
For perspective there is CreatePerspective. This creates a projection matrix, which is a specific kind of matrix for projecting a 3D scene onto a 2D display, so it is better used with vertices when setting (for example) BasicEffect.Projection. In this case you're best off doing proper 3D rendering.
For distort, just use vertices and place them manually wherever you need them.
I have a rotation-translation matrix [R T] (3x4).
Is there a function in opencv that performs the rotation-translation described by [R T]?
A lot of solutions to this question I think make hidden assumptions. I will try to give you a quick summary of how I think about this problem (I have had to think about it a lot in the past). Warping between two images is a 2 dimensional process accomplished by a 3x3 matrix called a homography. What you have is a 3x4 matrix which defines a transform in 3 dimensions. You can convert between the two by treating your image as a flat plane in 3 dimensional space. The trick then is to decide on the initial position in world space of your image plane. You can then transform its position and project it onto a new image plane with your camera intrinsics matrix.
The first step is to decide where your initial image lies in world space, note that this does not have to be the same as your initial R and T matrices specify. Those are in world coordinates, we are talking about the image created by that world, all the objects in the image have been flattened into a plane. The simplest decision here is to set the image at a fixed displacement on the z axis and no rotation. From this point on I will assume no rotation. If you would like to see the general case I can provide it but it is slightly more complicated.
Next you define the transform between your two images in 3d space. Since you have both transforms with respect to the same origin, the transform from [A] to [B] is the same as the transform from [A] to your origin, followed by the transform from the origin to [B]. You can get that by
transform = [B]*inverse([A])
Now conceptually what you need to do is to take your first image, project its pixels onto the geometric interpretation of your image in 3d space, then transform those pixels in 3d space by the transform above, then project them back onto a new 2d image with your camera matrix. Those steps need to be combined into a single 3x3 matrix.
cv::Matx33f convert_3x4_to_3x3(cv::Matx34f pose, cv::Matx33f camera_mat, float zpos)
{
//converted condenses the 3x4 matrix which transforms a point in world space
//to a 3x3 matrix which transforms a point in world space. Instead of
//multiplying pose by a 4x1 3d homogeneous vector, by specifying that the
//incoming 3d vectors will ALWAYS have a z coordinate of zpos, one can instead
//multiply converted by a homogeneous 2d vector and get the same output for x and y.
cv::Matx33f converted(pose(0,0),pose(0,1),pose(0,2)*zpos+pose(0,3),
pose(1,0),pose(1,1),pose(1,2)*zpos+pose(1,3),
pose(2,0),pose(2,1),pose(2,2)*zpos+pose(2,3));
//This matrix will take a homogeneous 2d coordinate and "projects" it onto a
//flat plane at zpos. The x and y components of the incoming homogeneous 2d
//coordinate will be correct, the z component is dropped.
cv::Matx33f projected(1,0,0,
0,1,0,
0,0,zpos);
projected = projected*camera_mat.inv();
//now we have the pieces. A matrix which can take an incoming 2d point, and
//convert it into a pseudo 3d point (x and y correspond to 3d, z is unused)
//and a matrix which can take our pseudo 3d point and transform it correctly.
//Now we just need to turn our transformed pseudo 3d point back into a 2d point
//in our new image, to do that simply multiply by the camera matrix.
return camera_mat*converted*projected;
}
This is probably a more complicated answer than you were looking for but I hope it gives you an idea of what you are asking. This can be very confusing and I glazed over some parts of it quickly, feel free to ask for clarification. If you need the solution to work without the assumption that the initial image appears without rotation let me know, I just didn't want to make it more complicated than it needed to be.
XNA contains a BoundingFrustum class which defines a frustum and facilitates collisions with Rays and other objects. However, the Frustum can only be constructed with a Matrix. I have a certain object which is created in a frustum shape using 8 vertices; what kind of Matrix should I create from these vertices in order to create a Frustum to represent it?
The object in question is a chunk of a sphere-- 4 points on the sphere's surface in the form of a square, extending downward into the origin of the sphere.
Normally to use a BoundingFrustum you pass it a Matrix that is a view matrix multiplied by a projection matrix:
BoundingFrustum frustum = new BoundingFrustum(this.viewMatrix * this.projectionMatrix);
There is no easy way to use that class to do what you describe unless you're particularly skilled in creating a Matrix by hand that combines what would normally be in a view matrix and projection matrix into something that represents your 8 corners.
What I would recommend is writing an algorithm to solve your problem.
// Do something like this for all 8 sides of the frustum, if the sphere lies outside
// of any of the 8 sides then it isn't in the frustum.
// Each plane will have a normal direction (the direction the inside is facing)
Vector3 normal = Vector3.UnitY;
// Creates a plane
Plane plane = new Plane(normal, 20.0f);
BoundingSphere sphere = new BoundingSphere(Vector3.Zero, 10.0f);
// This type is an enum that will tell you which side the intersection is on
PlaneIntersectionType type = sphere.Intersects(plane);
Thanks to Nic's inspiration and the help of a friend, I was able to write this class which represents a region defined by 8 points which has flat sides, such as a frustum or cube.
Here is the class.
It's important to note that, when passing in the constructor parameters, you choose a vantage point from which to view your region and stick with it.
Hope this helps anyone else who may run into this (obscure) problem to solve.
I have a sprite object in XNA.
It has a size, position and rotation.
How to translate a point from the screen coordinates to the sprite coordinates ?
Thanks,
SW
You need to calculate the transform matrix for your sprite, invert that (so the transform now goes from world space -> local space) and transform the mouse position by the inverted matrix.
Matrix transform = Matrix.CreateScale(scale) * Matrix.CreateRotationZ(rotation) * Matrix.CreateTranslation(translation);
Matrix inverseTransform = Matrix.Invert(transform);
Vector3 transformedMousePosition = Vector3.Transform(mousePosition, inverseTransform);
You might find the following XNA picking sample useful:
http://creators.xna.com/en-us/sample/picking
One solution is to hit test against the sprite's original, unrotated bounding box.
So given the 2D screen vector (x,y):
translate the 2D vector into local sprite space: (x,y) - (spritex,spritey)
apply inverse sprite rotation
perform hit testing against bounding box
The hit test can of course be made more accurate by taking into account the sprite shape.
I think it may be as simple as using the Contains method on Rectangle, the rectangle being the bounding box of your sprite. I've implemented drag-and-drop this way in XNA; I believe Contains tests based on x and y being screen coordinates.