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Projections ​

Projections transform spherical polygonal geometry to planar polygonal geometry. D3 provides implementations of several classes of standard projections:

For more projections, see d3-geo-projection and d3-geo-polygon. You can implement custom projections using geoProjection or geoProjectionMutator.

projection(point) ​

Source · Returns a new array [x, y] (typically in pixels) representing the projected point of the given point. The point must be specified as a two-element array [longitude, latitude] in degrees. May return null if the specified point has no defined projected position, such as when the point is outside the clipping bounds of the projection.

projection.invert(point) ​

Source · Returns a new array [longitude, latitude] in degrees representing the unprojected point of the given projected point. The point must be specified as a two-element array [x, y] (typically in pixels). May return null if the specified point has no defined projected position, such as when the point is outside the clipping bounds of the projection.

This method is only defined on invertible projections.

projection.stream(stream) ​

Source · Returns a projection stream for the specified output stream. Any input geometry is projected before being streamed to the output stream. A typical projection involves several geometry transformations: the input geometry is first converted to radians, rotated on three axes, clipped to the small circle or cut along the antimeridian, and lastly projected to the plane with adaptive resampling, scale and translation.

projection.preclip(preclip) ​

If preclip is specified, sets the projection’s spherical clipping to the specified function and returns the projection; preclip is a function that takes a projection stream and returns a clipped stream. If preclip is not specified, returns the current spherical clipping function. Preclipping is commonly used to cut along the antimeridian line or along a small circle.

projection.postclip(postclip) ​

If postclip is specified, sets the projection’s Cartesian clipping to the specified function and returns the projection; postclip is a function that takes a projection stream and returns a clipped stream. If postclip is not specified, returns the current Cartesian clipping function. Post-clipping occurs on the plane, when a projection is bounded to a certain extent such as a rectangle.

projection.clipAngle(angle) ​

Source · If angle is specified, sets the projection’s clipping circle radius to the specified angle in degrees and returns the projection. If angle is null, switches to antimeridian cutting rather than small-circle clipping. If angle is not specified, returns the current clip angle which defaults to null. Small-circle clipping is independent of viewport clipping via projection.clipExtent. See also projection.preclip, geoClipAntimeridian, geoClipCircle.

projection.clipExtent(extent) ​

Source · If extent is specified, sets the projection’s viewport clip extent to the specified bounds in pixels and returns the projection. The extent bounds are specified as an array [[x₀, y₀], [x₁, y₁]], where x₀ is the left-side of the viewport, y₀ is the top, x₁ is the right and y₁ is the bottom. If extent is null, no viewport clipping is performed. If extent is not specified, returns the current viewport clip extent which defaults to null. Viewport clipping is independent of small-circle clipping via projection.clipAngle. See also projection.postclip, geoClipRectangle.

projection.scale(scale) ​

Source · If scale is specified, sets the projection’s scale factor to the specified value and returns the projection. If scale is not specified, returns the current scale factor; the default scale is projection-specific. The scale factor corresponds linearly to the distance between projected points; however, absolute scale factors are not equivalent across projections.

projection.translate(translate) ​

Source · If translate is specified, sets the projection’s translation offset to the specified two-element array [tx, ty] and returns the projection. If translate is not specified, returns the current translation offset which defaults to [480, 250]. The translation offset determines the pixel coordinates of the projection’s center. The default translation offset places ⟨0°,0°⟩ at the center of a 960×500 area.

projection.center(center) ​

Source · If center is specified, sets the projection’s center to the specified center, a two-element array of [longitude, latitude] in degrees and returns the projection. If center is not specified, returns the current center, which defaults to ⟨0°,0°⟩.

projection.angle(angle) ​

Source · If angle is specified, sets the projection’s post-projection planar rotation angle to the specified angle in degrees and returns the projection. If angle is not specified, returns the projection’s current angle, which defaults to 0°. Note that it may be faster to rotate during rendering (e.g., using context.rotate) rather than during projection.

projection.reflectX(reflect) ​

If reflect is specified, sets whether or not the x-dimension is reflected (negated) in the output. If reflect is not specified, returns true if x-reflection is enabled, which defaults to false. This can be useful to display sky and astronomical data with the orb seen from below: right ascension (eastern direction) will point to the left when North is pointing up.

projection.reflectY(reflect) ​

If reflect is specified, sets whether or not the y-dimension is reflected (negated) in the output. If reflect is not specified, returns true if y-reflection is enabled, which defaults to false. This is especially useful for transforming from standard spatial reference systems, which treat positive y as pointing up, to display coordinate systems such as Canvas and SVG, which treat positive y as pointing down.

projection.rotate(angles) ​

Source · If rotation is specified, sets the projection’s three-axis spherical rotation to the specified angles, which must be a two- or three-element array of numbers [lambda, phi, gamma] specifying the rotation angles in degrees about each spherical axis. (These correspond to yaw, pitch and roll.) If the rotation angle gamma is omitted, it defaults to 0. See also geoRotation. If rotation is not specified, returns the current rotation which defaults [0, 0, 0].

projection.precision(precision) ​

Source · If precision is specified, sets the threshold for the projection’s adaptive resampling to the specified value in pixels and returns the projection. This value corresponds to the Douglas–Peucker distance. If precision is not specified, returns the projection’s current resampling precision which defaults to √0.5 ≅ 0.70710…

projection.fitExtent(extent, object) ​

Source · Sets the projection’s scale and translate to fit the specified GeoJSON object in the center of the given extent. The extent is specified as an array [[x₀, y₀], [x₁, y₁]], where x₀ is the left side of the bounding box, y₀ is the top, x₁ is the right and y₁ is the bottom. Returns the projection.

For example, to scale and translate the New Jersey State Plane projection to fit a GeoJSON object nj in the center of a 960×500 bounding box with 20 pixels of padding on each side:

js
var projection = d3.geoTransverseMercator()
    .rotate([74 + 30 / 60, -38 - 50 / 60])
    .fitExtent([[20, 20], [940, 480]], nj);

Any clip extent is ignored when determining the new scale and translate. The precision used to compute the bounding box of the given object is computed at an effective scale of 150.

projection.fitSize(size, object) ​

Source · A convenience method for projection.fitExtent where the top-left corner of the extent is [0, 0]. The following two statements are equivalent:

js
projection.fitExtent([[0, 0], [width, height]], object);
projection.fitSize([width, height], object);

projection.fitWidth(width, object) ​

Source · A convenience method for projection.fitSize where the height is automatically chosen from the aspect ratio of object and the given constraint on width.

projection.fitHeight(height, object) ​

Source · A convenience method for projection.fitSize where the width is automatically chosen from the aspect ratio of object and the given constraint on height.

Raw projections ​

Raw projections are point transformation functions that are used to implement custom projections; they typically passed to geoProjection or geoProjectionMutator. They are exposed here to facilitate the derivation of related projections. Raw projections take spherical coordinates [lambda, phi] in radians (not degrees!) and return a point [x, y], typically in the unit square centered around the origin.

project(lambda, phi) ​

Projects the specified point [lambda, phi] in radians, returning a new point [x, y] in unitless coordinates.

project.invert(x, y) ​

The inverse of project.

geoProjection(project) ​

Source · Constructs a new projection from the specified raw projection, project. The project function takes the longitude and latitude of a given point in radians, often referred to as lambda (λ) and phi (φ), and returns a two-element array [x, y] representing its unit projection. The project function does not need to scale or translate the point, as these are applied automatically by projection.scale, projection.translate, and projection.center. Likewise, the project function does not need to perform any spherical rotation, as projection.rotate is applied prior to projection.

For example, a spherical Mercator projection can be implemented as:

js
var mercator = d3.geoProjection(function(x, y) {
  return [x, Math.log(Math.tan(Math.PI / 4 + y / 2))];
});

If the project function exposes an invert method, the returned projection will also expose projection.invert.

geoProjectionMutator(factory) ​

Source · Constructs a new projection from the specified raw projection factory and returns a mutate function to call whenever the raw projection changes. The factory must return a raw projection. The returned mutate function returns the wrapped projection. For example, a conic projection typically has two configurable parallels. A suitable factory function, such as geoConicEqualAreaRaw, would have the form:

js
// y0 and y1 represent two parallels
function conicFactory(phi0, phi1) {
  return function conicRaw(lambda, phi) {
    return […, …];
  };
}

Using d3.geoProjectionMutator, you can implement a standard projection that allows the parallels to be changed, reassigning the raw projection used internally by geoProjection:

js
function conicCustom() {
  var phi0 = 29.5,
      phi1 = 45.5,
      mutate = d3.geoProjectionMutator(conicFactory),
      projection = mutate(phi0, phi1);

  projection.parallels = function(_) {
    return arguments.length ? mutate(phi0 = +_[0], phi1 = +_[1]) : [phi0, phi1];
  };

  return projection;
}

When creating a mutable projection, the mutate function is typically not exposed.

geoTransform(methods) ​

Source · Defines an arbitrary transform using the methods defined on the specified methods object. Any undefined methods will use pass-through methods that propagate inputs to the output stream.

For example, to reflect the y-dimension (see also projection.reflectY):

js
const reflectY = d3.geoTransform({
  point(x, y) {
    this.stream.point(x, -y);
  }
});

Or to define an affine matrix transformation:

js
function matrix(a, b, c, d, tx, ty) {
  return d3.geoTransform({
    point(x, y) {
      this.stream.point(a * x + b * y + tx, c * x + d * y + ty);
    }
  });
}

A transform is a generalized projection; it implements projection.stream and can be passed to path.projection. However, it implements only a subset of the other projection methods, and represent arbitrary geometric transformations rather than projections from spherical to planar coordinates.

geoIdentity() ​

Source · The identity transform can be used to scale, translate and clip planar geometry. It implements projection.scale, projection.translate, projection.fitExtent, projection.fitSize, projection.fitWidth, projection.fitHeight, projection.clipExtent, projection.angle, projection.reflectX and projection.reflectY.

geoClipAntimeridian ​

Source · A clipping function which transforms a stream such that geometries (lines or polygons) that cross the antimeridian line are cut in two, one on each side. Typically used for pre-clipping.

geoClipCircle(angle) ​

Source · Generates a clipping function which transforms a stream such that geometries are bounded by a small circle of radius angle around the projection’s center. Typically used for pre-clipping.

geoClipRectangle(x0, y0, x1, y1) ​

Source · Generates a clipping function which transforms a stream such that geometries are bounded by a rectangle of coordinates [[x0, y0], [x1, y1]]. Typically used for post-clipping.