Good tutorials or books on Quaternions

BlitzMax Forums/BlitzMax Programming/Good tutorials or books on Quaternions

* (Posted 2015) [#1]

Does anyone know of any good books or tutorials on Quaternions, what I'm aiming for is simple placement, movement, rotations and the tformpoint systems :)

BlitzSupport (Posted 2015) [#2]

The Blitz3D source ought to help, and I know there's stuff in the Code Archives relating to quaternions and their weird ilk. (If you want to actually learn it properly though, I've got nothing!)

Kryzon (Posted 2015) [#3]

I can't attest for their quality, but check out Jorge's "Math for Game Developers" series: http://youtube.com/channel/UCEhBM2x5MG9-e_JSOzU068ww There's also the Math & Physics article section from Gamedev.Net (which is where I found that video series above): http://www.gamedev.net/page/resources/_/technical/math-and-physics/

* (Posted 2015) [#4]

Ah thanks guys pulling apart the code archive sources already :)

* (Posted 2015) [#5]

This is even more confusing, some internet tutorials use xyzw others are applied to the sixteen float matrices :s @James: going through that to locate the sections I need at present and see if they can be adjusted to my requirements. @Kryzon: those are even more confusing lol I might have a serious look at the Warner minib3d adjustments as well to see if I can make head or tail of it all, if there was a easy to understand book on it I would be there :)

angros47 (Posted 2015) [#6]

Edzup, actually I am surprised you ask similar questions (a week ago you asked about how to get pitch in Euler rotations, and now this), because I thought you knew this argument very well: I remember that the first patch to fix TurnEntity in MiniB3D (using quaternions instead of Euler's) was made by you.

* (Posted 2015) [#7]

I think your mistaking me for Warner?

angros47 (Posted 2015) [#8]

No, I don't mistake you for Warner: Here is your code: http://www.blitzbasic.com/Community/post.php?topic=74382&post=832581 Here is Warner code: http://www.blitzbasic.com/codearcs/codearcs.php?code=2498 Your code is 8 years old, Warner's code (that I used in OpenB3D) is only 6 years old, so the first code is yours (I also ported it to C++, because I was considering using it in my version... )

* (Posted 2015) [#9]

Crikey I dont remember writing that lol Will use that in me new framework :)

JoshK (Posted 2015) [#10]

http://www.leadwerks.com/werkspace/page/api-reference/_/quat/ http://www.leadwerks.com/werkspace/page/api-reference/_/quat/quatslerp-r898 http://www.amazon.com/Visualizing-Quaternions-Kaufmann-Interactive-Technology/dp/0120884003

* (Posted 2015) [#11]

Thanks Josh will have a look :)

FBEpyon (Posted 2015) [#12]

@Edzup - Go here : http://blog.db-in.com/cameras-on-opengl-es-2-x/ this is where I learned everything I needed for a good camera system with Quaternions. I even wrote something up in Blitzmax : Function degreeToRad:Float(x:Float) Local kPI180:Float = 0.017453 Return x * kPI180 End Method Function radToDregree(x:Float) Local k180PI:Float = 57.295780 Return x * k180PI End Method Type Mat4 Field m:Float[16] End Type Function matIdentity(matrix:Mat4) 'First Column matrix.m[0] = 1.0 matrix.m[1] = 0.0 matrix.m[2] = 0.0 matrix.m[3] = 0.0 'Second Column matrix.m[4] = 0.0 matrix.m[5] = 1.0 matrix.m[6] = 0.0 matrix.m[7] = 0.0 'Third Column matrix.m[8] = 0.0 matrix.m[9] = 0.0 matrix.m[10] = 1.0 matrix.m[11] = 0.0 'Fourth Column matrix.m[12] = 0.0 matrix.m[13] = 0.0 matrix.m[14] = 0.0 matrix.m[15] = 1.0 End Function Function matTranslate(x:Float, y:Float, z:Float, matrix:Mat4) matIdentity(matrix) matrix.m[12] = x matrix.m[13] = y matrix.m[14] = z End Function Function matScale(sx:Float, sy:Float, sz:Float, matrix:Mat4) matIdentity(matrix) matrix.m[0] = sx matrix.m[5] = sy matrix.m[10] = sz End Function Function matRotateX(degree:Float, matrix:Mat4) Local radians:Float = Mat4.degreeToRad(degree) matIdentity(matrix) matrix.m[5] = cos(radians) matrix.m[6] = -sin(radians) matrix.m[9] = -matrix.m[6] matrix.m[10] = matrix.m[5] End Function Function matRotateY(degree:Float, matrix:Mat4) Local radians:Float = Mat4.degreeToRad(degree) matIdentity(matrix) matrix.m[0] = cos(radians) matrix.m[2] = sin(radians) matrix.m[8] = -matrix.m[2] matrix.m[10] = matrix.m[0] End Function Function matRotateZ(degree:Float, matrix:Mat4) Local radians:Float = Mat4.degreeToRad(degree) matIdentity(matrix) matrix.m[0] = cos(radians) matrix.m[1] = sin(radians) matrix.m[4] = -matrix.m[1] matrix.m[5] = matrix.m[0] End Function FUnction matMuliply(matrix1.Mat4, matrix2.Mat4, matrix:Mat4) matrix.m[0] = matrx1.m[0] * matrix2.m[0] + matrx1.m[4] * matrix2.m[1] + matrx1.m[8] * matrix2.m[2] + matrx1.m[12] * matrix2.m[3] matrix.m[1] = matrx1.m[1] * matrix2.m[0] + matrx1.m[5] * matrix2.m[1] + matrx1.m[9] * matrix2.m[2] + matrx1.m[13] * matrix2.m[3] matrix.m[2] = matrx1.m[2] * matrix2.m[0] + matrx1.m[6] * matrix2.m[1] + matrx1.m[10] * matrix2.m[2] + matrx1.m[14] * matrix2.m[3] matrix.m[3] = matrx1.m[3] * matrix2.m[0] + matrx1.m[7] * matrix2.m[1] + matrx1.m[11] * matrix2.m[2] + matrx1.m[15] * matrix2.m[3] matrix.m[4] = matrx1.m[0] * matrix2.m[4] + matrx1.m[4] * matrix2.m[5] + matrx1.m[8] * matrix2.m[6] + matrx1.m[12] * matrix2.m[7] matrix.m[5] = matrx1.m[1] * matrix2.m[4] + matrx1.m[5] * matrix2.m[5] + matrx1.m[9] * matrix2.m[6] + matrx1.m[13] * matrix2.m[7] matrix.m[6] = matrx1.m[2] * matrix2.m[4] + matrx1.m[6] * matrix2.m[5] + matrx1.m[10] * matrix2.m[6] + matrx1.m[14] * matrix2.m[7] matrix.m[7] = matrx1.m[3] * matrix2.m[4] + matrx1.m[7] * matrix2.m[5] + matrx1.m[11] * matrix2.m[6] + matrx1.m[15] * matrix2.m[7] matrix.m[8] = matrx1.m[0] * matrix2.m[8] + matrx1.m[4] * matrix2.m[9] + matrx1.m[8] * matrix2.m[10] + matrx1.m[12] * matrix2.m[11] matrix.m[9] = matrx1.m[1] * matrix2.m[8] + matrx1.m[5] * matrix2.m[9] + matrx1.m[9] * matrix2.m[10] + matrx1.m[13] * matrix2.m[11] matrix.m[10] = matrx1.m[2] * matrix2.m[8] + matrx1.m[6] * matrix2.m[9] + matrx1.m[10] * matrix2.m[10] + matrx1.m[14] * matrix2.m[11] matrix.m[11] = matrx1.m[3] * matrix2.m[8] + matrx1.m[7] * matrix2.m[9] + matrx1.m[11] * matrix2.m[10] + matrx1.m[15] * matrix2.m[11] matrix.m[12] = matrx1.m[0] * matrix2.m[12] + matrx1.m[4] * matrix2.m[13] + matrx1.m[8] * matrix2.m[14] + matrx1.m[12] * matrix2.m[15] matrix.m[13] = matrx1.m[1] * matrix2.m[12] + matrx1.m[5] * matrix2.m[13] + matrx1.m[9] * matrix2.m[14] + matrx1.m[13] * matrix2.m[15] matrix.m[14] = matrx1.m[2] * matrix2.m[12] + matrx1.m[6] * matrix2.m[13] + matrx1.m[10] * matrix2.m[14] + matrx1.m[14] * matrix2.m[15] matrix.m[15] = matrx1.m[3] * matrix2.m[12] + matrx1.m[7] * matrix2.m[13] + matrx1.m[11] * matrix2.m[14] + matrx1.m[15] * matrix2.m[15] End Function Type Quaternion Field x:Float, y:Float, z:Float, w:Float End Type Function quatToMatrix(q:Quaternion, matrix:Mat4) matrix.m[0] = 1 - 2 * (q.y * q.y + q.z + q.z) matrix.m[1] = 2 * (q.x * q.y + q.z * q.w) matrix.m[2] = 2 * (q.x * q.z - q.y * q.w) matrix.m[3] = 0 matrix.m[4] = 2 * (q.x * q.y - q.z * q.w) matrix.m[5] = 1 - 2 * (q.x * q.x + q.z * q.z) matrix.m[6] = 2 * (q.z * q.y + q.z * q.w) matrix.m[7] = 0 matrix.m[8] = 2 * (q.x * q.z + q.y * q.w) matrix.m[9] = 2 * (q.y * q.z - q.x * q.w) matrix.m[10] = 1 - 2 * (q.x * q.x + q.y * q.y) matrix.m[11] = 0 matrix.m[12] = 0 matrix.m[13] = 0 matrix.m[14] = 0 matrix.m[15] = 1 End Function Function quatMultiply(q1:Quaternion, q2:Quaternion, q:Quaternion) q.w = q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z q.x = q1.w * q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y q.y = q1.w * q2.y - q1.x * q2.z + q1.y * q2.w + q1.z * q2.x q.z = q1.w * q2.z + q1.x * q2.y - q1.y * q2.x + q1.z * q2.w End Function Function quatIdentity(q:Quaternion) q.x = 0 q.y = 0 q.z = 0 q.w = 0 End Function Function quatInverse(q:Quaternion) q.x :* -1 q.y :* -1 q.z :* -1 End Function Function quatNormalize(q:Quaternion) 'Not Yet Resovled End Function Function quatAxis:Quaternion(v:Vector, degrees:Float) Local q:Quaternion = New Quaternion Local radians:Float = degreeToRad(degrees) Local s:Float = Sin(radians * 0.5) Local c:Float = Cos(radians * 0.5) q.w = c q.x = v.x * s q.y = v.y * s q.z = v.x * s Return q End Function Function quatEuler:Quaternion(degreesX:Float, degreesY:Float, degreesZ:Float) Local q:Quaternion = New Quaternion Local radiansY:Float = degreeToRad(degreesY) Local radiansZ:Float = degreeToRad(degreesZ) Local radiansX:Float = degreesToRad(degreezX) Local sY:Float = Sin(radiansY * 0.5) Local cY:Float = Cos(radiansY * 0.5) Local sZ:Float = Sin(radiansZ * 0.5) Local cZ:Float = Cos(radiansZ * 0.5) Local sX:Float = Sin(radiansX * 0.5) Local xC:Float = Cos(radiansX * 0.5) q.w = cY * cZ * cX - sY * sZ * sX q.x = sY * sZ * cX + cY * cZ * sX q.y = sY * cZ * cX + cY * sZ * sX q.z = cY * sZ * cX - sY * cZ * sX Return q End Function Function OrthoM(near:Float, far:Float, left:Float, right:Float, bottom:Float, top:Float, matrix:Mat4) matrix.m[0] = 2.0 / (right - left) matrix.m[1] = 0.0 matrix.m[2] = 0.0 matrix.m[3] = 0.0 matrix.m[4] = 0.0 matrix.m[5] = 2.0 / (top - bottom) matrix.m[6] = 0.0 matrix.m[7] = 0.0 matrix.m[8] = 0.0 matrix.m[9] = 0.0 matrix.m[10] = -2.0 / (far - near) matrix.m[11] = 0.0 matrix.m[12] = -(right + left) / (right - left) matrix.m[13] = -(top + bottom) / (top - bottom) matrix.m[14] = -(far + near) / (far - near) matrix.m[15] = 1 End Function Function FrustumM(near:Float, far:Float, aov:Float, aspect:Float, matrix:Mat4) Local size:Float = near * tan(degreeToRad(aov) / 2.0) Local left:Float = -size Local right:Float = size Local bottom:Float = -size/aspect Local top:Float = size/aspect matrix.m[0] = 2.0 * near / (right - left) matrix.m[1] = 0.0 matrix.m[2] = 0.0 matrix.m[3] = 0.0 matrix.m[4] = 0.0 matrix.m[5] = 2.0 * near / (top - bottom) matrix.m[6] = 0.0 matrix.m[7] = 0.0 matrix.m[8] = (right + left) / (right - left) matrix.m[9] = (top + bottom) / (top - bottom) matrix.m[10] = -(far + near) / (far - near) matrix.m[11] = -1.0 matrix.m[12] = 0.0 matrix.m[13] = 0.0 matrix.m[14] = -(2.0 * far * near) / (far / near) matrix.m[15] = 0.0 End Function Type Vector Field x:Float, y:Float, z:Float Method Set:Vec3(x:Float, y:Float, z:Float) Self.x = x Self.y = y Self.z = z End Method Method Length:Float() Return Sqr(x * x + y * y + z * z) End Method Method Normalize() Self.x = Self.x / Self.Length() Self.y = Self.y / Self.Length() Self.z = Self.z / Self.Length() End Method End Type Function vectorAdd(v1:Vector, v2:Vector, v:Vector) v.x = v1.x + v2.x v.y = v1.y + v2.y v.z = v1.z + v2.z End Function Function vectorSub(v1:Vector, v2:Vector, v:Vector) v.x = v1.x - v2.x v.y = v1.y - v2.y v.z = v1.z - v2.z End Function Function vectorScalor(v1:Vector, s:Float, v:Vector) v.x = v1.x * s v.y = v1.y * s v.z = v1.z * s End Function Type Camera Field position:Vector Field rotation:Vector Field matTranslate:Mat4 Field matRotateX:Mat4 Field matRotateY:Mat4 Field matRotateZ:Mat4 End Type Function Createcamera:Camera(x:Float, y:Float, z:Float, rx:Float, ry:Float, rz:Float) Local cam:Camera = New Camera cam.position = New Vector cam.position.Set(x, y, z) cam.rotation = New Vector cam.rotation.Set(rx, ry, rz) Return Camera End Function Function RotateCamera(cam:Camera, rx:Float, ry:Float, rz:Float) cam.rotation.Set(rx, ry, rz) End Function Function TranslateCamera(cam:Camera, x:Float, y:Float, z:Float) cam.position.Set(x, y, z) End Function Never finished it though... FBEpyon

* (Posted 2015) [#13]

Thanks Fbepyon that is a great help :)

Yahfree (Posted 2015) [#14]

Quaternions is a pretty complicated number system (involving a real scalar component and a 3D imaginary vector), they are an extension of complex numbers. There are some good videos on youtube about why they work, and their various interesting properties: https://www.youtube.com/watch?v=mHVwd8gYLnI You can (if you wish) dive into the math and understand the WHY, or you can do as most do and treat them as a black box tool that accomplishes nicely interpolated, gimbal-lock free rotations.

* (Posted 2015) [#15]

I think once they are in the engine I wont visit them again, my engine is nodular so it will work with all othee systems :)