I have a small game level laid out with a cartesian coordinate system. I have a camera class that I want to translate all of the points from cartesian space to isometric space using this matrix:
[cos(45), sin(45)]
[-sin(45), cos(45)]
On paper, multiplying any vector by the matrix successfully puts that vector into the isometric space after the first rotation.
Right now, I am only able to get the level to draw according to the cameras position using this matrix:
public Matrix GetTransformation()
{
_mTransform =
Matrix.CreateTranslation(-Position.X, -Position.Y, 0);
return _mTransform;
}
Where I am confused is where the matrix I listed above fits into that equation.
CameraIso2D takes no parameters, but here is the Draw function
public void Draw(SpriteBatch sb)
{
// Start drawing from this GameLayer
sb.Begin(
SpriteSortMode.FrontToBack,
BlendState.AlphaBlend,
null,
null,
null,
null,
_transformation);
// Draw all contained objects
foreach (DrawableGameObject dgo in _drawableGameObjects)
dgo.Draw(sb);
// End drawing from this GameLayer
sb.End();
}
_transformation is the matrix _mTransform returned from CameraIso2D every update
I solved this by using two matrices. The first matrix uses the regular camera transformation and is passed into spriteBatch.Begin as the transformation matrix. For the isometric transformation matrix, I used Matrix.CreateRotationZ to mimic the isometric Y axis rotation, and then I used Matrix.CreateScale to mimic the isometric rotation down from the Y axis. GameObjects need a position for cartesian coordinates, and a vector2 for their isometric coordinates. Pass the GameObject's cartesian coordinates through the isometric transformation matrix to get the isometric coordinates, and then draw to that location.
Related
I have a 360 spherical video. I use this video as a texture on a sphere in Unity. Inside the sphere is a camera and this functions as the setup for my Virtual Reality experience. Pretty basic.
I am trying to write a bit of code on the web where people can upload 360 images and videos, place a marker/hotspot on the 360 spherical image/video, and then apply the image/video-texture on the sphere in Unity3D. If I overlay a simple x/y coordinate grid on the 360 video/image-texture, put in some x/y-coordinates to place the marker/hotspot, and put the texture back on the sphere, Unity will not interpret this correctly since we are now in 3D space and we are looking at the texture from within the sphere mapped onto the plane with all the distortion happening.
My question is, how do I convert these x and y coordinates on the 2D plane of the 360 video texture to coordinates that can be understood in 3D within Unity3D?
My first thought was to use 2-dimensional cartesian coordinates and convert these into spherical coordinates, but I seem to be missing a z-axis in the cartesian coordinates to make this work.
Is the z-axis simply 0 or is it the radius from center of the sphere to the x/y-coordinate? What does the z-axis represent? Is there maybe two coordinate systems. One that is coordinates on a plane and one that is from the centre of the sphere?
This is the conversion code that I have so far:
public static void CartesianToSpherical(Vector3 cartCoords, out float outRadius, out float outPolar, out float outElevation){
if (cartCoords.x == 0)
cartCoords.x = Mathf.Epsilon;
outRadius = Mathf.Sqrt((cartCoords.x * cartCoords.x)
+ (cartCoords.y * cartCoords.y)
+ (cartCoords.z * cartCoords.z));
outPolar = Mathf.Atan(cartCoords.z / cartCoords.x);
if (cartCoords.x < 0)
outPolar += Mathf.PI;
outElevation = Mathf.Asin(cartCoords.y / outRadius);
}
This is my very first post so please excuse me if I am doing anything wrong and let me know how to improve.
Spherical co-ordinates are different from 2d or 3d co-ordinates as you need to measure them in radians. It is usually measured from the center of the sphere and XY axis. It marks a rectangular area on the surface of the sphere. Please refer to this link for spherical co-ordinates in unity - https://blog.nobel-joergensen.com/2010/10/22/spherical-coordinates-in-unity/
I'm trying to rotate a bounding box in xna, this is how I usually do it:
new Rectangle((int)position.X, (int)position.Y, (int)texture.Width, (int)texture.Height);
but It currently does not return the rotation that is in my draw code:
spriteBatch.Draw(texture, position, null, Color.White, rotation, origin, scale, SpriteEffects.None, 1f);
how do I rotate it with the player? I was trying to figure this out and stumbled across this:
2D BoundingRectangle rotation in XNA 4.0
but I'm not quite sure how to implement the Matrices he's talking about,and I'm making a 2d game as opposed to the 3d one here.
The Rectangle structure is an axis aligned bounding rectangle. The sides will always be parallel to the X and Y axes. If you want a rotated bounding rectangle you have to implement it yourself.
One algorithm for calculating collision of rotated rectangles is the Separating Axis Theorem.
Matrices are, as stated in the linked answer, essential in computer graphics. You can rotate a shape by rotating each of its vertices with the same rotation matrix. This is the general rotation matrix for two dimensions:
Matrices are then "applied" to vectors with matrix-vector multiplication:
which equals
I struggled with this problem for two days before finding the solution
Rotating bounding box
Hope this will help !
I have three Vector3 points in 3D space. I need to copy the rotation (the tangent?) of this triangle to the orientation of a 3D model. How can I calculate the triangles Vector3 tangent or create a rotation matrix out of those points?
Finding the angle of a triangle is described here: Find the normal angle of the face of a triangle in 3D, given the co-ordinates of its vertices
Suppose you find the normal and call it N'. It should be trivial for you to write the normal of the "unrotated" triangle, N, eg <1, 0, 0>. It should also be trivial to figure out how to rotate from N to N' and you can create a rotation matrix for it with Matrix.CreateFromAxisAngle in XNA. This matrix should rotate everything like you want.
I'm trying to create an isometric (35 degrees) view by using a camera.
I'm drawing a triangle which rotates around Z axis.
For some reason the triangle is being cut at a certain point of the rotation
giving this result
I calculate the camera position by angle and z distance
using this site: http://www.easycalculation.com/trigonometry/triangle-angles.php
This is how I define the camera:
// isometric angle is 35.2ยบ => for -14.1759f Y = 10 Z
Vector3 camPos = new Vector3(0, -14.1759f, 10f);
Vector3 lookAt = new Vector3(0, 0, 0);
viewMat = Matrix.CreateLookAt(camPos, lookAt, Vector3.Up);
//projectionMatrix = Matrix.CreatePerspectiveFieldOfView(MathHelper.PiOver4, Game.GraphicsDevice.Viewport.AspectRatio, 1, 100);
float width = GameInterface.vpMissionWindow.Width;
float height = GameInterface.vpMissionWindow.Height;
projMat = Matrix.CreateOrthographic(width, height, 1, 1000);
worldMat = Matrix.Identity;
This is how I recalculate the world matrix rotation:
worldMat = Matrix.CreateRotationZ(3* visionAngle);
// keep triangle arround this Center point
worldMat *= Matrix.CreateTranslation(center);
effect.Parameters["xWorld"].SetValue(worldMat);
// updating rotation angle
visionAngle += 0.005f;
Any idea what I might be doing wrong? This is my first time working on a 3D project.
Your triangle is being clipped by the far-plane.
When your GPU renders stuff, it only renders pixels that fall within the range (-1, -1, 0) to (1, 1, 1). That is: between the bottom left of the viewport and the top right. But also between some "near" plane and some "far" plane on the Z axis. (As well as doing clipping, this also determines the range of values covered by the depth buffer.)
Your projection matrix takes vertices that are in world or view space, and transforms them so that they fit inside that raster space. You may have seen the standard image of a view frustum for a perspective projection matrix, that shows how the edges of that raster region appear when transformed back into world space. The same thing exists for orthographic projections, but the edges of the view region are parallel.
The simple answer is to increase the distance to your far plane so that all your geometry falls within the raster region. It is the fourth parameter to Matrix.CreateOrthographic.
Increasing the distance between your near and far plane will reduce the precision of your depth buffer - so avoid making it any bigger than you need it to be.
I think your far plane is cropping it, so you should make bigger the projection matrix far plane argument...
projMat = Matrix.CreateOrthographic(width, height, 1, 10000);
I'm working on opengl project.
I set up perspective projection and render a transformed rectangle (rotated, scaled)
How i can calculate rectangle's bounding box (rectangle position,size)
Thank you
You'd run the rectangle through the same matrices that OpenGL does to transform the 3D points into 2D screen-space ones. Get your input vectors, multiply them by any that you want to apply to the object, ModelView matrix, Projection matrix, then you have screen-space coords. Then check whether the resulting coordinates are on-screen, then you can calculate the minimum/maximum X and Y coordinates, and you have your bounding rectangle.
See also here (9.100), if you've got the GLU utility library functions available:
http://www.opengl.org/resources/faq/technical/transformations.htm
Hope that helps.