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Math 3D.pck.st
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Math 3D.pck.st
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'From Cuis 5.0 [latest update: #4370] on 4 September 2020 at 11:11:58 am'!
'Description Stuff from Balloon3D-Math by Andreas Raab. Adapted to use 64-bit Float arithmetic (in addition to 32-bit FloatArray).'!
!provides: 'Math 3D' 1 24!
SystemOrganization addCategory: #'Math 3D'!
!classDefinition: #Float32Matrix3x3 category: #'Math 3D'!
Float32Array variableWordSubclass: #Float32Matrix3x3
instanceVariableNames: ''
classVariableNames: 'Float32Matrix3x3Identity Float32Matrix3x3Zero'
poolDictionaries: ''
category: 'Math 3D'!
!classDefinition: 'Float32Matrix3x3 class' category: #'Math 3D'!
Float32Matrix3x3 class
instanceVariableNames: ''!
!classDefinition: #Float32Vector3 category: #'Math 3D'!
Float32Array variableWordSubclass: #Float32Vector3
instanceVariableNames: ''
classVariableNames: ''
poolDictionaries: ''
category: 'Math 3D'!
!classDefinition: 'Float32Vector3 class' category: #'Math 3D'!
Float32Vector3 class
instanceVariableNames: ''!
!classDefinition: #Float64Color4 category: #'Math 3D'!
Float64Array variableWordSubclass: #Float64Color4
instanceVariableNames: ''
classVariableNames: ''
poolDictionaries: ''
category: 'Math 3D'!
!classDefinition: 'Float64Color4 class' category: #'Math 3D'!
Float64Color4 class
instanceVariableNames: ''!
!classDefinition: #Float64Matrix3x3 category: #'Math 3D'!
Float64Array variableWordSubclass: #Float64Matrix3x3
instanceVariableNames: ''
classVariableNames: 'Float64Matrix3x3Identity Float64Matrix3x3Zero'
poolDictionaries: ''
category: 'Math 3D'!
!classDefinition: 'Float64Matrix3x3 class' category: #'Math 3D'!
Float64Matrix3x3 class
instanceVariableNames: ''!
!classDefinition: #Float64Matrix4x4 category: #'Math 3D'!
Float64Array variableWordSubclass: #Float64Matrix4x4
instanceVariableNames: ''
classVariableNames: 'Float64Matrix4x4Identity Float64Matrix4x4Zero'
poolDictionaries: ''
category: 'Math 3D'!
!classDefinition: 'Float64Matrix4x4 class' category: #'Math 3D'!
Float64Matrix4x4 class
instanceVariableNames: ''!
!classDefinition: #Float64Quaternion category: #'Math 3D'!
Float64Array variableWordSubclass: #Float64Quaternion
instanceVariableNames: ''
classVariableNames: 'Float64IdentityRotation Identity'
poolDictionaries: ''
category: 'Math 3D'!
!classDefinition: 'Float64Quaternion class' category: #'Math 3D'!
Float64Quaternion class
instanceVariableNames: ''!
!classDefinition: #Float64Vector2 category: #'Math 3D'!
Float64Array variableWordSubclass: #Float64Vector2
instanceVariableNames: ''
classVariableNames: ''
poolDictionaries: ''
category: 'Math 3D'!
!classDefinition: 'Float64Vector2 class' category: #'Math 3D'!
Float64Vector2 class
instanceVariableNames: ''!
!classDefinition: #Float64Vector3 category: #'Math 3D'!
Float64Array variableWordSubclass: #Float64Vector3
instanceVariableNames: ''
classVariableNames: ''
poolDictionaries: ''
category: 'Math 3D'!
!classDefinition: 'Float64Vector3 class' category: #'Math 3D'!
Float64Vector3 class
instanceVariableNames: ''!
!classDefinition: #Float64Vector4 category: #'Math 3D'!
Float64Array variableWordSubclass: #Float64Vector4
instanceVariableNames: ''
classVariableNames: ''
poolDictionaries: ''
category: 'Math 3D'!
!classDefinition: 'Float64Vector4 class' category: #'Math 3D'!
Float64Vector4 class
instanceVariableNames: ''!
!Float32Matrix3x3 commentStamp: '<historical>' prior: 0!
I represent a 3x3 matrix for linear transformations (rotation and scale, maybe also skew) commonly used in 3D computer graphics.
Based on Float64Matrix3x3, but 32 bits.!
!Float32Vector3 commentStamp: '<historical>' prior: 0!
I represent simple (x, y, z) 3D Cartesian coordinates with 32-bit Float precision.
Based on Float64Vector3!
!Float64Color4 commentStamp: '<historical>' prior: 0!
I represent an RGBA color value in floating point format. I am used during the lighting and shading computations.
A copy of B3DColor4 (from Balloon3D-Math), but with 64 bit Float elements (instead of 32 bit Float).!
!Float64Matrix3x3 commentStamp: '<historical>' prior: 0!
I represent a 3x3 matrix for linear transformations (rotation and scale, maybe also skew) commonly used in 3D computer graphics.
Based on Float64Matrix4x4, but without a displacement.
Currently pretty bare bones. If more stuff from FloatMatrix4x4 is needed, consider making FloatMatrix4x4 a subclass of us, or maybe add a common subclass, to avoid code duplication.!
!Float64Matrix4x4 commentStamp: '<historical>' prior: 0!
I represent a general 4x4 transformation matrix commonly used in computer graphics.
A copy of B3DMatrix4x4 (from Balloon3D-Math), but with 64 bit Float elements (instead of 32 bit Float).!
!Float64Quaternion commentStamp: 'jmv 10/11/2016 10:41:38' prior: 0!
I represent general 3d rotations by using Unit-Quaternions. Unit-Quaternions are one of the best available representation for rotations in computer graphics because they provide an easy way of doing arithmetic with them and also because they allow us to use spherical linear interpolation (so-called "slerps") of rotations.
Indexed Variables:
a <Float> the real part of the quaternion. Scalar component, related to angle of rotation. Also called q0 or q4.
b <Float> the first imaginary part of the quaternion. Related to X coordinate of the rotation axis. Also called q1.
c <Float> the second imaginary part of the quaternion. Related to Y coordinate of the rotation axis. Also called q2.
d <Float> the third imaginary part of the quaternion. Related to Z coordinate of the rotation axis. Also called q3.
Started as a copy of B3DRotation (from Balloon3D-Math), but with 64 bit Float elements (instead of 32 bit Float).
See #a:b:c:d: , #q1:q2:q3:q4: and #x:y:z:a:
See http://bicycle.tudelft.nl/schwab/Publications/quaternion.pdf
See http://tutis.ca/Rotate/7quaternions.htm
Quaternions are used to state the attitude of an aircraft or spaceship with respect to a reference frame.
The reference frame might be ECEF cartesian coordinates (origin at Earth center, +x towards 0° lat, 0° lon, +y towards 0° lat, 90° lon east, +z towards North pole.
The "Body" coordinates have origin at center of mass of aircraft, +x points forward (nose of the plane), +y points to the right, +z points downwards.
The attitude is usually specified as "Inertial to Body" or "ECEF to Body" meaning a quaterion that if applied to the ECEF cartesian axes the result is the Body axes expressed in ECEF coordinates.
If what we want is to convert a direction or point in ECEF coordinates to Body coordinates, then the rotation is the reverse of the required to convert the axes.
See #rotate:, #bodyToInertial: and #inertialToBody:!
!Float64Vector2 commentStamp: '<historical>' prior: 0!
I represent simple (x, y) 2D Cartesian coordinates with 64-bit Float (a.k.a. double) precision.
Based on B3DVector2 (from Balloon3D-Math), but with 64 bit Float elements (instead of 32 bit Float).!
!Float64Vector3 commentStamp: '<historical>' prior: 0!
I represent simple (x, y, z) 3D Cartesian coordinates with 64-bit Float (a.k.a. double) precision.
Based on B3DVector3 (from Balloon3D-Math), but with 64 bit Float elements (instead of 32 bit Float).!
!Float64Vector4 commentStamp: '<historical>' prior: 0!
I represent 3D points in homogenous coordinates.
A copy of B3DVector4 (from Balloon3D-Math), but with 64 bit Float elements (instead of 32 bit Float).!
!Float32Matrix3x3 methodsFor: 'printing' stamp: 'jmv 11/24/2015 16:30'!
printOn: aStream
aStream newLine.
1 to: 3 do: [ :i |
aStream nextPutAll: '| '.
1 to: 3 do: [ :j |
(self at: i at: j) printOn: aStream integerDigits: 1 fractionDigits: 3.
aStream space ].
aStream nextPut: $|; newLine ]! !
!Float32Vector3 methodsFor: 'printing' stamp: 'jmv 3/16/2016 14:18'!
printOn: aStream
"The receiver prints on aStream in terms of infix notation."
self x printOn: aStream.
aStream nextPut: $@.
self y printOn: aStream.
aStream nextPut: $@.
self z printOn: aStream! !
!Float64Matrix3x3 methodsFor: 'printing' stamp: 'jmv 11/24/2015 10:09'!
printOn: aStream
aStream newLine.
1 to: 3 do: [ :i |
aStream nextPutAll: '| '.
1 to: 3 do: [ :j |
(self at: i at: j) printOn: aStream integerDigits: 1 fractionDigits: 3.
aStream space ].
aStream nextPut: $|; newLine ]! !
!Float64Matrix4x4 methodsFor: 'printing' stamp: 'jmv 7/3/2015 12:53'!
printOn: aStream
aStream newLine.
1 to: 4 do: [ :i |
aStream nextPutAll: '| '.
1 to: 4 do: [ :j |
(self at: i at: j) printOn: aStream integerDigits: 1 fractionDigits: 3.
aStream space ].
aStream nextPut: $|; newLine ]! !
!Float64Quaternion methodsFor: 'printing' stamp: 'jmv 7/13/2017 09:26:35'!
printOn: aStream
aStream
nextPutAll: self class name;
nextPut:$(;
print: self angleDegrees;
nextPut: Character space;
print: self axis;
nextPut:$).! !
!Float64Vector3 methodsFor: 'private' stamp: 'jmv 3/16/2016 14:18'!
printOn: aStream
"The receiver prints on aStream in terms of infix notation."
self x printOn: aStream.
aStream nextPut: $@.
self y printOn: aStream.
aStream nextPut: $@.
self z printOn: aStream! !
!Float32Matrix3x3 methodsFor: 'printing' stamp: 'jmv 11/24/2015 16:30'!
print
self printOn: Transcript.
Transcript newLine! !
!Float32Matrix3x3 methodsFor: 'arithmetic' stamp: 'jmv 9/3/2020 18:34:33'!
* aFloatVector3
"Answer the result of multiplying self by an argument vector"
| x y z rx ry rz |
"It would be nice to have a plugin for this...
<primitive: 'Float32MultiplyByVector' module: 'Squeak3D'>"
x := aFloatVector3 x.
y := aFloatVector3 y.
z := aFloatVector3 z.
rx := (x * self a11) + (y * self a12) + (z * self a13).
ry := (x * self a21) + (y * self a22) + (z * self a23).
rz := (x * self a31) + (y * self a32) + (z * self a33).
^Float32Vector3 x: rx y: ry z: rz! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a11
"Return the element a11"
^self at: 1! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a11: aNumber
"Store the element a11"
self at: 1 put: aNumber! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a12
"Return the element a12"
^self at: 2! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a12: aNumber
"Store the element a12"
self at: 2 put: aNumber! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a13
"Return the element a13"
^self at: 3! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a13: aNumber
"Store the element a13"
self at: 3 put: aNumber! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a21
"Return the element a21"
^self at: 4! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a21: aNumber
"Store the element a21"
self at: 4 put: aNumber! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a22
"Return the element a22"
^self at: 5! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a22: aNumber
"Store the element a22"
self at: 5 put: aNumber! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a23
"Return the element a23"
^self at: 6! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a23: aNumber
"Store the element a23"
self at: 6 put: aNumber! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a31
"Return the element a31"
^self at: 7! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a31: aNumber
"Store the element a31"
self at: 7 put: aNumber! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a32
"Return the element a32"
^self at: 8! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a32: aNumber
"Store the element a32"
self at: 8 put: aNumber! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a33
"Return the element a33"
^self at: 9! !
!Float32Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 16:30'!
a33: aNumber
"Store the element a33"
self at: 9 put: aNumber! !
!Float32Matrix3x3 methodsFor: 'accessing' stamp: 'jmv 11/24/2015 16:30'!
at: i at: j
^ self at: ((i - 1) * 3 + j).
! !
!Float32Matrix3x3 methodsFor: 'accessing' stamp: 'jmv 11/24/2015 16:30'!
at: i at: j put: aValue
^ self at: ((i - 1) * 3 + j) put: aValue.
! !
!Float32Matrix3x3 methodsFor: 'testing' stamp: 'jmv 11/24/2015 16:31'!
isIdentity
^self = Float32Matrix3x3Identity! !
!Float32Matrix3x3 methodsFor: 'testing' stamp: 'jmv 11/24/2015 16:31'!
isZero
^self = Float32Matrix3x3Zero! !
!Float32Matrix3x3 methodsFor: 'transforming' stamp: 'jmv 11/24/2015 16:30'!
localDirToGlobal: aVector
"Multiply direction vector with the receiver"
^self * aVector! !
!Float32Matrix3x3 methodsFor: 'initialize' stamp: 'jmv 11/24/2015 16:31'!
setIdentity
"Set the receiver to the identity matrix"
self loadFrom: Float32Matrix3x3Identity! !
!Float32Matrix3x3 methodsFor: 'initialize' stamp: 'jmv 11/24/2015 16:30'!
setScale: aVector
self
a11: aVector x;
a22: aVector y;
a33: aVector z! !
!Float32Matrix3x3 methodsFor: 'initialize' stamp: 'jmv 11/24/2015 16:31'!
setZero
"Set the receiver to the zero matrix"
self loadFrom: Float32Matrix3x3Zero! !
!Float32Matrix3x3 class methodsFor: 'instance creation' stamp: 'jmv 11/24/2015 16:30'!
identity
^self new setIdentity! !
!Float32Matrix3x3 class methodsFor: 'instance creation' stamp: 'jmv 11/24/2015 16:30'!
numElements
^9! !
!Float32Matrix3x3 class methodsFor: 'instance creation' stamp: 'jmv 11/24/2015 16:30'!
withScale: amount
^self identity setScale: amount! !
!Float32Matrix3x3 class methodsFor: 'instance creation' stamp: 'jmv 11/24/2015 16:30'!
zero
^self new! !
!Float32Matrix3x3 class methodsFor: 'class initialization' stamp: 'jmv 11/24/2015 16:31'!
initialize
"Float32Matrix3x3 initialize"
Float32Matrix3x3Zero := self new.
Float32Matrix3x3Identity := self new.
Float32Matrix3x3Identity a11: 1.0; a22: 1.0; a33: 1.0! !
!Float32Vector3 methodsFor: 'vector functions' stamp: 'jmv 11/24/2015 16:32'!
normalize
self /= self length! !
!Float32Vector3 methodsFor: 'vector functions' stamp: 'jmv 11/24/2015 16:32'!
normalized
^self / self length! !
!Float32Vector3 methodsFor: 'vector functions' stamp: 'jmv 11/24/2015 16:32'!
safelyNormalize
"Safely normalize the receiver, e.g. check if the length is non-zero"
| length |
length := self length.
length = 1.0 ifTrue:[^self].
length = 0.0 ifFalse:[self /= length].! !
!Float32Vector3 methodsFor: 'vector functions' stamp: 'jmv 11/24/2015 16:32'!
safelyNormalized
"Safely normalize the receiver, e.g. check if the length is non-zero"
^self copy safelyNormalize! !
!Float32Vector3 methodsFor: 'private' stamp: 'jmv 11/24/2015 16:32'!
privateLoadFrom: srcObject
self x: srcObject x y: srcObject y z: srcObject z.! !
!Float32Vector3 methodsFor: 'accessing' stamp: 'jmv 11/24/2015 16:32'!
x
^self at: 1! !
!Float32Vector3 methodsFor: 'accessing' stamp: 'jmv 11/24/2015 16:32'!
x: aFloat
self at: 1 put: aFloat! !
!Float32Vector3 methodsFor: 'accessing' stamp: 'jmv 11/24/2015 16:32'!
y
^self at: 2! !
!Float32Vector3 methodsFor: 'accessing' stamp: 'jmv 11/24/2015 16:32'!
y: aFloat
self at: 2 put: aFloat! !
!Float32Vector3 methodsFor: 'accessing' stamp: 'jmv 11/24/2015 16:32'!
z
^self at: 3! !
!Float32Vector3 methodsFor: 'accessing' stamp: 'jmv 11/24/2015 16:33'!
z: aFloat
self at: 3 put: aFloat! !
!Float32Vector3 methodsFor: 'initialize' stamp: 'jmv 11/24/2015 16:33'!
x: x y: y z: z
self x: x.
self y: y.
self z: z.! !
!Float32Vector3 class methodsFor: 'instance creation' stamp: 'jmv 11/24/2015 16:33'!
numElements
^3! !
!Float32Vector3 class methodsFor: 'instance creation' stamp: 'jmv 11/24/2015 16:33'!
value: aFloat
^self x: aFloat y: aFloat z: aFloat! !
!Float32Vector3 class methodsFor: 'instance creation' stamp: 'jmv 11/24/2015 16:33'!
x: x y: y z: z
^self new x: x y: y z: z! !
!Float32Vector3 class methodsFor: 'instance creation' stamp: 'jmv 11/24/2015 16:33'!
zero
^self new! !
!Float64Color4 methodsFor: 'accessing'!
alpha
^self floatAt: 4! !
!Float64Color4 methodsFor: 'accessing'!
alpha: aNumber
self floatAt: 4 put: aNumber! !
!Float64Color4 methodsFor: 'accessing'!
blue
^self floatAt: 3! !
!Float64Color4 methodsFor: 'accessing'!
blue: aNumber
self floatAt: 3 put: aNumber! !
!Float64Color4 methodsFor: 'accessing'!
green
^self floatAt: 2! !
!Float64Color4 methodsFor: 'accessing'!
green: aNumber
self floatAt: 2 put: aNumber! !
!Float64Color4 methodsFor: 'accessing'!
red
^self floatAt: 1! !
!Float64Color4 methodsFor: 'accessing'!
red: aNumber
self floatAt: 1 put: aNumber! !
!Float64Color4 methodsFor: 'converting'!
asColor
^Color r: self red g: self green b: self blue alpha: self alpha! !
!Float64Color4 methodsFor: 'converting' stamp: 'ar 5/4/2000 17:59'!
asFloat64Color
^self! !
!Float64Color4 methodsFor: 'converting' stamp: 'ar 2/4/1999 20:21'!
pixelValue32
^self asColor pixelWordForDepth: 32! !
!Float64Color4 methodsFor: 'interpolating' stamp: 'jsp 2/8/1999 19:57'!
interpolateTo: end at: amountDone
"Return the color vector yielded by interpolating from the state of the object to the specified end state at the specified amount done"
| newColor r g b a |
r := self red.
g := self green.
b := self blue.
a := self alpha.
newColor := Float64Color4 new.
newColor red: r + (((end red) - r) * amountDone).
newColor green: g + (((end green) - g) * amountDone).
newColor blue: b + (((end blue) - b) * amountDone).
newColor alpha: a + (((end alpha) - a) * amountDone).
^ newColor.
! !
!Float64Color4 methodsFor: 'testing' stamp: 'ar 2/15/1999 22:12'!
isZero
^self alpha isZero! !
!Float64Color4 methodsFor: 'private' stamp: 'jmv 2/26/2015 11:57'!
privateLoadFrom: aColor
self red: aColor red.
self green: aColor green.
self blue: aColor blue.
self alpha: aColor alpha.! !
!Float64Color4 methodsFor: 'initialize' stamp: 'ar 2/7/1999 16:21'!
r: rValue g: gValue b: bValue a: aValue
self red: rValue.
self green: gValue.
self blue: bValue.
self alpha: aValue.! !
!Float64Color4 class methodsFor: 'instance creation' stamp: 'ar 2/1/1999 21:22'!
numElements
^4! !
!Float64Color4 class methodsFor: 'instance creation' stamp: 'ar 2/7/1999 16:21'!
r: rValue g: gValue b: bValue a: aValue
^self new r: rValue g: gValue b: bValue a: aValue! !
!Float64Color4 class methodsFor: 'instance creation' stamp: 'jsp 2/8/1999 18:46'!
red: r green: g blue: b alpha: a
"Create an initialize a color vector."
| newColor |
newColor := Float64Color4 new.
newColor red: r.
newColor green: g.
newColor blue: b.
newColor alpha: a.
^ newColor.
! !
!Float64Matrix3x3 methodsFor: 'printing' stamp: 'jmv 11/24/2015 09:54'!
print
self printOn: Transcript.
Transcript newLine! !
!Float64Matrix3x3 methodsFor: 'arithmetic' stamp: 'jmv 11/24/2015 11:35'!
* aFloat64Vector3
"Answer the result of multiplying self by an argument vector"
| x y z rx ry rz |
"It would be nice to have a plugin for this...
<primitive: 'Float64MultiplyByVector' module: 'Squeak3D'>"
self flag: #Float64Primitive.
x := aFloat64Vector3 x.
y := aFloat64Vector3 y.
z := aFloat64Vector3 z.
rx := (x * self a11) + (y * self a12) + (z * self a13).
ry := (x * self a21) + (y * self a22) + (z * self a23).
rz := (x * self a31) + (y * self a32) + (z * self a33).
^Float64Vector3 x: rx y: ry z: rz! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 09:54'!
a11
"Return the element a11"
^self at: 1! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 09:54'!
a11: aNumber
"Store the element a11"
self at: 1 put: aNumber! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 09:54'!
a12
"Return the element a12"
^self at: 2! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 09:54'!
a12: aNumber
"Store the element a12"
self at: 2 put: aNumber! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 09:54'!
a13
"Return the element a13"
^self at: 3! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 09:54'!
a13: aNumber
"Store the element a13"
self at: 3 put: aNumber! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 10:06'!
a21
"Return the element a21"
^self at: 4! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 10:06'!
a21: aNumber
"Store the element a21"
self at: 4 put: aNumber! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 10:06'!
a22
"Return the element a22"
^self at: 5! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 10:06'!
a22: aNumber
"Store the element a22"
self at: 5 put: aNumber! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 10:06'!
a23
"Return the element a23"
^self at: 6! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 10:06'!
a23: aNumber
"Store the element a23"
self at: 6 put: aNumber! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 10:06'!
a31
"Return the element a31"
^self at: 7! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 10:07'!
a31: aNumber
"Store the element a31"
self at: 7 put: aNumber! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 10:07'!
a32
"Return the element a32"
^self at: 8! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 10:07'!
a32: aNumber
"Store the element a32"
self at: 8 put: aNumber! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 10:07'!
a33
"Return the element a33"
^self at: 9! !
!Float64Matrix3x3 methodsFor: 'element-access' stamp: 'jmv 11/24/2015 10:07'!
a33: aNumber
"Store the element a33"
self at: 9 put: aNumber! !
!Float64Matrix3x3 methodsFor: 'converting' stamp: 'jmv 11/26/2015 15:09'!
asIEEE32BitPrecisionFloat
| answer |
answer _ Float32Matrix3x3 new.
1 to: 9 do: [ :i | answer at: i put: (self at: i) ].
^answer! !
!Float64Matrix3x3 methodsFor: 'accessing' stamp: 'jmv 11/24/2015 10:09'!
at: i at: j
^ self at: ((i - 1) * 3 + j).
! !
!Float64Matrix3x3 methodsFor: 'accessing' stamp: 'jmv 11/24/2015 10:09'!
at: i at: j put: aValue
^ self at: ((i - 1) * 3 + j) put: aValue.
! !
!Float64Matrix3x3 methodsFor: 'testing' stamp: 'jmv 11/24/2015 09:56'!
isIdentity
^self = Float64Matrix3x3Identity! !
!Float64Matrix3x3 methodsFor: 'testing' stamp: 'jmv 11/24/2015 09:57'!
isZero
^self = Float64Matrix3x3Zero! !
!Float64Matrix3x3 methodsFor: 'transforming' stamp: 'jmv 11/24/2015 11:35'!
localDirToGlobal: aVector
"Multiply direction vector with the receiver"
^self * aVector! !
!Float64Matrix3x3 methodsFor: 'initialize' stamp: 'jmv 11/24/2015 09:56'!
setIdentity
"Set the receiver to the identity matrix"
self loadFrom: Float64Matrix3x3Identity! !
!Float64Matrix3x3 methodsFor: 'initialize' stamp: 'jmv 11/24/2015 09:54'!
setScale: aVector
self
a11: aVector x;
a22: aVector y;
a33: aVector z! !
!Float64Matrix3x3 methodsFor: 'initialize' stamp: 'jmv 11/24/2015 09:57'!
setZero
"Set the receiver to the zero matrix"
self loadFrom: Float64Matrix3x3Zero! !
!Float64Matrix3x3 class methodsFor: 'instance creation' stamp: 'jmv 11/24/2015 09:54'!
identity
^self new setIdentity! !
!Float64Matrix3x3 class methodsFor: 'instance creation' stamp: 'jmv 11/24/2015 09:58'!
numElements
^9! !
!Float64Matrix3x3 class methodsFor: 'instance creation' stamp: 'jmv 11/24/2015 10:03'!
withScale: amount
^self identity setScale: amount! !
!Float64Matrix3x3 class methodsFor: 'instance creation' stamp: 'jmv 11/24/2015 09:54'!
zero
^self new! !
!Float64Matrix3x3 class methodsFor: 'class initialization' stamp: 'jmv 11/24/2015 10:16'!
initialize
"Float64Matrix3x3 initialize"
Float64Matrix3x3Zero := self new.
Float64Matrix3x3Identity := self new.
Float64Matrix3x3Identity a11: 1.0; a22: 1.0; a33: 1.0! !
!Float64Matrix4x4 methodsFor: 'printing' stamp: 'jmv 7/13/2015 10:10'!
print
self printOn: Transcript.
Transcript newLine! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a11
"Return the element a11"
^self at: 1! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a11: aNumber
"Store the element a11"
self at: 1 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a12
"Return the element a12"
^self at: 2! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a12: aNumber
"Store the element a12"
self at: 2 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a13
"Return the element a13"
^self at: 3! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a13: aNumber
"Store the element a13"
self at: 3 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a14
"Return the element a14"
^self at: 4! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a14: aNumber
"Store the element a14"
self at: 4 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a21
"Return the element a21"
^self at: 5! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a21: aNumber
"Store the element a21"
self at: 5 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a22
"Return the element a22"
^self at: 6! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a22: aNumber
"Store the element a22"
self at: 6 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a23
"Return the element a23"
^self at: 7! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a23: aNumber
"Store the element a23"
self at: 7 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a24
"Return the element a24"
^self at: 8! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a24: aNumber
"Store the element a24"
self at: 8 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a31
"Return the element a31"
^self at: 9! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a31: aNumber
"Store the element a31"
self at: 9 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a32
"Return the element a32"
^self at: 10! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a32: aNumber
"Store the element a32"
self at: 10 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a33
"Return the element a33"
^self at: 11! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a33: aNumber
"Store the element a33"
self at: 11 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a34
"Return the element a34"
^self at: 12! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a34: aNumber
"Store the element a34"
self at: 12 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a41
"Return the element a41"
^self at: 13! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a41: aNumber
"Store the element a41"
self at: 13 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a42
"Return the element a42"
^self at: 14! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a42: aNumber
"Store the element a42"
self at: 14 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a43
"Return the element a43"
^self at: 15! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a43: aNumber
"Store the element a43"
self at: 15 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:29'!
a44
"Return the element a44"
^self at: 16! !
!Float64Matrix4x4 methodsFor: 'element-access' stamp: 'ar 2/1/1999 21:28'!
a44: aNumber
"Store the element a44"
self at: 16 put: aNumber! !
!Float64Matrix4x4 methodsFor: 'accessing' stamp: 'jsp 2/25/1999 13:58'!
alternateRotation
"Return the angular rotation around each axis of the matrix"
| cp sp cy sy cr sr vAngles |
vAngles := Float64Vector3 new.
((self a13) = 0) ifTrue: [ ((self a33) >= 0) ifTrue: [ vAngles at: 2 put: 0.
cr := (self a11).
sr := (self a12).
cp := (self a33). ]
ifFalse: [ vAngles at: 2 put: (Float pi).
cr := (self a11) negated.
sr := (self a12) negated.
cp := (self a33) negated. ]
]
ifFalse: [
vAngles at: 2 put: (((self a13) negated) arcTan: (self a33)).
cy := (vAngles at: 3) cos.
sy := (vAngles at: 3) sin.
cr := (cy * (self a11)) + (sy * (self a31)).
sr := (cy* (self a12)) + (sy * (self a32)).
cp := (cy * (self a33)) - (sy * (self a13)).
].
sp := (self a23).
vAngles at: 1 put: (sp arcTan: cp).
vAngles at: 3 put: (sr arcTan: cr).
vAngles at: 1 put: ((vAngles at: 1) radiansToDegrees).
vAngles at: 2 put: ((vAngles at: 2) radiansToDegrees).
vAngles at: 3 put: ((vAngles at: 3) radiansToDegrees).
^ vAngles.
! !
!Float64Matrix4x4 methodsFor: 'accessing' stamp: 'jsp 2/11/1999 14:09'!
at: i at: j
^ self at: ((i - 1) * 4 + j).
! !
!Float64Matrix4x4 methodsFor: 'accessing' stamp: 'jsp 2/11/1999 14:09'!
at: i at: j put: aValue
^ self at: ((i - 1) * 4 + j) put: aValue.
! !
!Float64Matrix4x4 methodsFor: 'accessing' stamp: 'jmv 2/26/2015 16:09'!
pitchYawRoll
"Assume the receiver describes an orthonormal 3x3 matrix, i.e. a pure 3D rotation"
| pitch yaw roll |
pitch := self a23 negated arcSin.
yaw := self a13 arcTan: self a33.
roll := self a21 arcTan: self a22.
^pitch radiansToDegrees@yaw radiansToDegrees@roll radiansToDegrees! !
!Float64Matrix4x4 methodsFor: 'accessing' stamp: 'jmv 2/26/2015 16:10'!
pitchYawRoll: ypr
"Assume the receiver describes an orthonormal 3x3 matrix, i.e. a pure 3D rotation
plus a translation"
| offset mx my mz |
offset := self translation.
mx := self class identity rotationAroundX: ypr x.
my := self class identity rotationAroundY: ypr y.
mz := self class identity rotationAroundZ: ypr z.
self loadFrom: (mz composeWith: (my composeWith: mx)).
self translation: offset
! !
!Float64Matrix4x4 methodsFor: 'accessing' stamp: 'jsp 2/25/1999 13:58'!
rotation
"Return the angular rotation around each axis of the matrix"
| vRow1 vRow2 vRow3 vScale vShear vAngles vRowCross determinate |
vRow1 := self row1.
vRow2 := self row2.
vRow3 := self row3.
vScale := Float64Vector3 new.
vShear := Float64Vector3 new.
vAngles := Float64Vector3 new.