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 <transform-function> CSS数据类型用于对元素的显示做变换。通常,这种变换可以由矩阵表示,并且可以使用每个点上的矩阵乘法来确定所得到的图像。

2D图形 的坐标系统

目前有多种用来描述转换坐标模型,最常用的是 笛卡尔坐标系统齐次坐标

笛卡尔 坐标

在笛卡尔坐标系中,每个 欧氏空间 里的点都由横坐标和纵坐标这两个值来确定。 在CSS(和大部分的计算机图形学)中,原点 (0, 0) 在元素的左上角。每个点都使用数学上的向量符号(x,y)来描述。

每个线性函数使用 2 × 2 矩阵描述,如:

                                                                                          a   c
                                                                                          b   d

 

将矩阵乘法用于上述坐标系中的每个点,一个变换就形成了:

.

可以在一行中进行多次矩阵乘法进行变换:

.
 

有了这种方法,就可以描述大部分常见的变换并因此可以将他们组合起来,如:旋转、缩放或拉伸。(事实上,所有线性函数的变换都可以被描述。)组合的变换是从右到左生效的。然而,有一种常见的变换并不是线性的,所以当这种变换要用这种方法来表示时,应该被单独列出来:位移。位移的向量 (tx, ty) 必须单独表示,作为两个附加参数。

奥古斯特·费迪南德·莫比乌斯 的 齐次坐标系 表示了一个 3 × 3 的变换矩阵,虽然它对于非专业的人来说更复杂和少见,这并不影响将它表示为线性函数,并且这样就不需要考虑额外的特例。

3D 图形的坐标

转换函数的定义

matrix()

CSS 函数 matrix() 用六个指定的值来指定一个均匀的二维(2D)变换矩阵。这个矩形中的常量值是不作为参数进行传递的,其他的参数则在主要列的顺序中描述。

matrix(a, b, c, d, tx, ty)matrix3d(a, b, 0, 0, c, d, 0, 0, 0, 0, 1, 0, tx, ty, 0, 1) 的简写

注意:直到火狐浏览器的 16 版本, Gecko 内核才为 txty 兼容了  <length> 这个数据格式。

语法

matrix(a, b, c, d, tx, ty)

属性值

a b c d
以 <number> 的格式来描述线性变换
tx ty
以 <number> 的格式来描述变换的量

笛卡尔坐标系中用二阶矩阵表示的点坐标

齐次坐标系中用三阶矩阵表示的点坐标

笛卡尔坐标系中用三阶矩阵表示的点坐标

齐次坐标系中用四阶矩阵表示的点坐标
              a c
               b  d
           a c ty
            b  d  tx
            0  0  1
             a c ty
              b  d  tx
              0  0  1
          a c 0 tx
           b  d  0  ty
           0  0  1  0
           0  0  0  1
 [a b c d tx ty]

matrix3d()

CSS 函数 matrix3d() 用一个 4 × 4 的齐次矩阵来描述一个三维(3D)变换。16个参数都在主要列的顺序中描述。

注意:直到火狐浏览器的 16 版本, Gecko 内核才为 a4, b4c4兼容了  <length> 这个数据格式。

语法

matrix3d(a1, b1, c1, d1, a2, b2, c2, d2, a3, b3, c3, d3, a4, b4, c4, d4)

属性值

a1 b1 c1 d1 a2 b2 c2 d2 a3 b3 c3 d3 d4
以 <number> 的格式来描述线性变换
a4 b4 c4
以 <number> 的格式来描述变换的量

笛卡尔坐标系中用二阶矩阵表示的点坐标

齐次坐标系中用三阶矩阵表示的点坐标

笛卡尔坐标系中用三阶矩阵表示的点坐标

齐次坐标系中用四阶矩阵表示的点坐标

这个变换是属于 3D 空间的,并不适用于这两种情况。

笛卡尔坐标矩阵不允许由一般的三维仿射变换来作为平移,因为平移不是线性变换。 a1  a2  a3  a4b1  b2  b3  b4
c1     c2     c3     c4
d1     d2    d3    d4

perspective()

The perspective() CSS function defines the distance between the z=0 plane and the user in order to give to the 3D-positioned element some perspective. Each 3D element with z>0 becomes larger; each 3D-element with z<0 becomes smaller. The strength of the effect is determined by the value of this property.

Syntax

perspective(l)

Values

l
Is a <length> giving the distance from the user to the z=0 plane. It is used to apply a perspective transform to the element. If it is 0 or a negative value, no perspective transform is applied.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3

This transform applies to the 3D space and cannot be represented on the plan.

A perspective is not a linear transform in ℝ3 and cannot be represented using a matrix in the Cartesian coordinates system. 100001000010001/d1

rotate()

The rotate() CSS function defines a transformation that moves the element around a fixed point (as specified by the transform-origin property) without deforming it. The amount of movement is defined by the specified angle; if positive, the movement will be clockwise, if negative, it will be counter-clockwise. A rotation by 180° is called point reflection.

Syntax

rotate(a)

Values

a
Is an <angle> representing the angle of the rotation. A positive angle denotes a clockwise rotation, a negative angle a counter-clockwise one.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3
cos(a)-sin(a) sin(a)cos(a) cos(a)-sin(a)0sin(a)cos(a)0001 cos(a)-sin(a)0sin(a)cos(a)0001 cos(a)-sin(a)00sin(a)cos(a)0000100001
[cos(a) sin(a) -sin(a) cos(a) 0 0]

rotate3d()

The rotate3d()CSS function defines a transformation that moves the element around a fixed axis without deforming it. The amount of movement is defined by the specified angle; if positive, the movement will be clockwise, if negative, it will be counter-clockwise.

In the 3D space, rotations have three degrees of liberty, describing an axis of rotation. The axis of rotation is defined by an [x, y, z] vector and pass by the origin (as defined by the transform-origin CSS property. If the vector is not normalized, that is the sum of the square of its three coordinates is not 1, it will be normalized internally. A non-normalizable vector, like the null vector, [0, 0, 0], will cause the rotation not to be applied, without invaliding the whole CSS property.

In opposition to rotations in the plane, the composition of 3D rotations is usually not commutative; it means that the order in which the rotations are applied is crucial.

Syntax

rotate3d(x, y, z, a)

Values

x
Is a <number> describing the x-coordinate of the vector denoting the axis of rotation.
y
Is a <number> describing the y-coordinate of the vector denoting the axis of rotation.
z
Is a <number> describing the z-coordinate of the vector denoting the axis of rotation.
a
Is an <angle> representing the angle of the rotation. A positive angle denotes a clockwise rotation, a negative angle a counter-clockwise one.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3
This transform applies to the 3D space and cannot be represented on the plane. 1+(1-cos(a))(x2-1)z·sin(a)+xy(1-cos(a))-y·sin(a)+xz·(1-cos(a))-z·sin(a)+xy·(1-cos(a))1+(1-cos(a))(y2-1)x·sin(a)+yz·(1-cos(a))ysin(a) + xz(1-cos(a))-xsin(a)+yz(1-cos(a))1+(1-cos(a))(z2-1)t0001

rotateX()

The rotateX()CSS function defines a transformation that moves the element around the abscissa without deforming it. The amount of movement is defined by the specified angle; if positive, the movement will be clockwise, if negative, it will be counter-clockwise.

The axis of rotation passes by the origin, defined by transform-origin CSS property.

rotateX(a)is a shorthand for rotate3D(1, 0, 0, a).

In opposition to rotations in the plane, the composition of 3D rotations is usually not commutative; it means that the order in which the rotations are applied is crucial.

Syntax

rotateX(a)

Values

a
Is an <angle> representing the angle of the rotation. A positive angle denotes a clockwise rotation, a negative angle a counter-clockwise one.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3
This transform applies to the 3D space and cannot be represented on the plane. 1000cos(a)-sin(a)0sin(a)cos(a) 10000cos(a)-sin(a)00sin(a)cos(a)00001

rotateY()

The rotateY()CSS function defines a transformation that moves the element around the ordinate without deforming it. The amount of movement is defined by the specified angle; if positive, the movement will be clockwise, if negative, it will be counter-clockwise.

The axis of rotation passes by the origin, defined by transform-origin CSS property.

rotateY(a)is a shorthand for rotate3D(0, 1, 0, a).

In opposition to rotations in the plane, the composition of 3D rotations is usually not commutative; it means that the order in which the rotations are applied is crucial.

Syntax

rotateY(a)

Values

a
Is an <angle> representing the angle of the rotation. A positive angle denotes a clockwise rotation, a negative angle a counter-clockwise one.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3
This transform applies to the 3D space and cannot be represented on the plane. cos(a)0sin(a)010-sin(a)0cos(a) cos(a)0sin(a)00100-sin(a)0cos(a)00001

rotateZ()

The rotateZ()CSS function defines a transformation that moves the element around the z-axis without deforming it. The amount of movement is defined by the specified angle; if positive, the movement will be clockwise, if negative, it will be counter-clockwise.

The axis of rotation passes by the origin, defined by transform-origin CSS property.

rotateZ(a)is a shorthand for rotate3D(0, 0, 1, a).

In opposition to rotations in the plane, the composition of 3D rotations is usually not commutative; it means that the order in which the rotations are applied is crucial.

Syntax

rotateZ(a)

Values

a
Is an <angle> representing the angle of the rotation. A positive angle denotes a clockwise rotation, a negative angle a counter-clockwise one.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3
This transform applies to the 3D space and cannot be represented on the plane. cos(a)-sin(a)0sin(a)cos(a)0001 cos(a)-sin(a)00sin(a)cos(a)0000000001

scale()

The scale() CSS function modifies the size of the element. It can either augment or decrease its size and as the amount of scaling is defined by a vector, it can do so more in one direction than in another one.

This transformation is characterized by a vector whose coordinates define how much scaling is done in each direction. If both coordinates of the vector are equal, the scaling is uniform, or isotropic, and the shape of the element is preserved. In that case, the scaling function defines a homothetic transformation.

When outside the ]-1, 1[ range, the scaling enlarges the element in the direction of the coordinate; when inside the range, it shrinks the element in that direction. When equal to 1 it does nothing and when negative it performs a point reflection and the size modification.

The scale() function only applies the transformation in the Euclidian plane (in 2D). To scale in the space, the scale3D() function has to be used.

Syntax

scale(sx) or
scale(sx, sy)

Values

sx
Is a <number> representing the abscissa of the scaling vector.
sy
Is a <number> representing the ordinate of the scaling vector. If not present, its default value is sx, leading to a uniform scaling preserving the shape of the element.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3
sx0 0sy sx000sy0001 sx000sy0001 sx0000sy0000100001
[sx 0 0 sy 0 0]

scale3d()

The scale3d() CSS function modifies the size of an element. Because the amount of scaling is defined by a vector, it can resize different dimensions at different scales.

This transformation is characterized by a vector whose coordinates define how much scaling is done in each direction. If all three coordinates of the vector are equal, the scaling is uniform, or isotropic, and the shape of the element is preserved. In that case, the scaling function defines a homothetic transformation.

When outside the [-1, 1] range, the scaling enlarges the element in the direction of the coordinate; when inside the range, it shrinks the element in that direction. When equal to 1 it does nothing and when negative it performs a point reflection and the size modification.

Syntax

scale3d(sx, sy, sz)

Values

sx
Is a <number> representing the abscissa of the scaling vector.
sy
Is a <number> representing the ordinate of the scaling vector.
sz
Is a <number> representing the z-component of the scaling vector.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3
This transform applies to the 3D space and cannot be represented on the plane. sx000sy000sz sx0000sy0000sz00001

scaleX()

The scaleX() CSS function modifies the abscissa of each element point by a constant factor, except if this scale factor is 1, in which case the function is the identity transform. The scaling is not isotropic and the angles of the element are not conserved.

scaleX(sx) is a shorthand for scale(sx, 1) or for scale3d(sx, 1, 1).

scaleX(-1) defines an axial symmetry with a vertical axis passing by the origin (as specified by the transform-origin property).

Syntax

scaleX(s)

Values

s
Is a <number> representing the scaling factor to apply on the abscissa of each point of the element.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3
s0 01 s00010001 s00010001 s000010000100001
[s 0 0 1 0 0]

scaleY()

The scaleY() CSS function modifies the ordinate of each element point by a constant factor except if this scale factor is 1, in which case the function is the identity transform. The scaling is not isotropic and the angles of the element are not conserved.

scaleY(sy) is a shorthand for scale(1, sy) or for scale3d(1, sy, 1).

scaleY(-1) defines an axial symmetry with a horizontal axis passing by the origin (as specified by the transform-origin property).

Syntax

scaleY(s)

Values

s
Is a <number> representing the scaling factor to apply on the ordinate of each point of the element.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3
10 0s 1000s0001 1000s0001 10000s0000100001
[1 0 0 s 0 0]

scaleZ()

The scaleZ() CSS function modifies the z-coordinate of each element point by a constant factor, except if this scale factor is 1, in which case the function is the identity transform. The scaling is not isotropic and the angles of the element are not conserved.

scaleZ(sz) is a shorthand for scale3d(1, 1, sz).

scaleZ(-1) defines an axial symmetry along the z-axis passing by the origin (as specified by the transform-origin property).

Syntax

scaleZ(s)

Values

s
Is a <number> representing the scaling factor to apply on the z-coordinate of each point of the element.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3
This transform applies to the 3D space and cannot be represented on the plane. 10001000s 1000010000s00001

skew()

The skew() CSS function is a shear mapping, or transvection, distorting each point of an element by a certain angle in each direction. It is done by increasing each coordinate by a value proportionate to the specified angle and to the distance to the origin. The more far from the origin, the more away the point is, the greater will be the value added to it.

Syntax

skew(ax)       or
skew(ax, ay)

Values

ax
Is an <angle> representing the angle to use to distort the element along the abscissa.
ay
Is an <angle> representing the angle to use to distort the element along the ordinate.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3
1tan(ax)tan(ay)1 1tan(ax)0tan(ay)10001 1tan(ax)0tan(ay)10001 1tan(ax)00tan(ay)10000100001
[1 tan(ay) tan(ax) 1 0 0]

skewX()

The skewX() CSS function is a horizontal shear mapping distorting each point of an element by a certain angle in the horizontal direction. It is done by increasing the abscissa coordinate by a value proportionate to the specified angle and to the distance to the origin. The more far from the origin, the more away the point is, the greater will be the value added to it.

Syntax

skewX(a)

Values

a
Is an <angle> representing the angle to use to distort the element along the abscissa.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3
1tan(ay)01 1tan(ay)0010001 1tan(ay)0010001 1tan(ay)00010000100001
[1 0 tan(a) 1 0 0]

skewY()

The skewY() CSS function is a vertical shear mapping distorting each point of an element by a certain angle in the vertical direction. It is done by increasing the ordinate coordinate by a value proportionate to the specified angle and to the distance to the origin. The more far from the origin, the more away the point is, the greater will be the value added to it.

Syntax

skewY(a)

Values

a
Is an <angle> representing the angle to use to distort the element along the ordinate.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3
10tan(ax)1 100tan(ax)10001 100tan(ax)10001 1000tan(ax)10000100001
[1 tan(a) 0 1 0 0]

translate()

The translate() CSS function moves the position of the element on the plane. This transformation is characterized by a vector whose coordinates define how much it moves in each direction.

Syntax

translate(tx)       or
translate(tx, ty)

Values

tx
Is a <length> representing the abscissa of the translating vector.
ty
Is a <length> representing the ordinate of the translating vector. If missing, it is assumed to be equals to txtranslate(2) means translate(2, 2).
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3

A translation is not a linear transform in ℝ2 and cannot be represented using a matrix in the cartesian coordinates system.

10tx01ty001 10tx01ty001 100tx010ty00100001
[1 0 0 1 tx ty]

translate3d()

The translate3d() CSS function moves the position of the element in the 3D space. This transformation is characterized by a 3-dimension vector whose coordinates define how much it moves in each direction.

Syntax

translate3d(tx, ty, tz)

Values

tx
Is a <length> representing the abscissa of the translating vector.
ty
Is a <length> representing the ordinate of the translating vector.
tz
Is a <length> representing the z component of the translating vector. It can't be a <percentage> value; in that case the property containing the transform is considered invalid.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3

This transform applies to the 3D space and cannot be represented on the plane.

A translation is not a linear transform in ℝ3 and cannot be represented using a matrix in the Cartesian coordinates system. 100tx010ty001tz0001

translateX()

The translateX() CSS function moves the element horizontally on the plane. This transformation is characterized by a <length> defining how much it moves horizontally.

translateX(tx) is a shortcut for translate(tx, 0).

Syntax

translateX(t)

Values

t
Is a <length> representing the abscissa of the translating vector.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3

A translation is not a linear transform in ℝ2 and cannot be represented using a matrix in the cartesian coordinates system.

10t010001 10t010001 100t010000100001
[1 0 0 1 t 0]

translateY()

The translateY() CSS function moves the element vertically on the plane. This transformation is characterized by a <length> defining how much it moves vertically.

translateY(ty) is a shortcut for translate(0, ty).

Syntax

translateY(t)

Values

t
Is a <length> representing the z-component of the translating vector. It can't be a <percentage> value; in that case the property containing the transform is considered invalid.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3

A translation is not a linear transform in ℝ2 and cannot be represented using a matrix in the cartesian coordinates system.

10001t001 10001t001 1000010t00100001
[1 0 0 1 0 t]

translateZ()

The translateZ() CSS function moves the element along the z-axis of the 3D space. This transformation is characterized by a <length> defining how much it moves.

translateZ(tz) is a shorthand for translate3d(0, 0, tz).

Syntax

translateZ(t)

Values

t
Is a <length> representing the ordinate of the translating vector.
Cartesian coordinates on ℝ2 Homogeneous coordinates on ℝℙ2 Cartesian coordinates on ℝ3 Homogeneous coordinates on ℝℙ3
This transform applies to the 3D space and cannot be represented on the plane. A translation is not a linear transform in ℝ3 and cannot be represented using a matrix in the Cartesian coordinates system. 10000100001t0001

 

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