diff --git a/app-proto/src/display.rs b/app-proto/src/display.rs
index 7256c60..51b207d 100644
--- a/app-proto/src/display.rs
+++ b/app-proto/src/display.rs
@@ -92,7 +92,7 @@ pub trait DisplayItem {
     // the smallest positive depth, represented as a multiple of `dir`, where
     // the line generated by `dir` hits the element. returns `None` if the line
     // misses the element
-    fn cast(&self, dir: Vector3<f64>, assembly_to_world: &DMatrix<f64>) -> Option<f64>;
+    fn cast(&self, dir: Vector3<f64>, assembly_to_world: &DMatrix<f64>, pixel_size: f64) -> Option<f64>;
 }
 
 impl DisplayItem for Sphere {
@@ -106,7 +106,7 @@ impl DisplayItem for Sphere {
     
     // this method should be kept synchronized with `sphere_cast` in
     // `spheres.frag`, which does essentially the same thing on the GPU side
-    fn cast(&self, dir: Vector3<f64>, assembly_to_world: &DMatrix<f64>) -> Option<f64> {
+    fn cast(&self, dir: Vector3<f64>, assembly_to_world: &DMatrix<f64>, _pixel_size: f64) -> Option<f64> {
         // if `a/b` is less than this threshold, we approximate
         // `a*u^2 + b*u + c` by the linear function `b*u + c`
         const DEG_THRESHOLD: f64 = 1e-9;
@@ -155,8 +155,30 @@ impl DisplayItem for Point {
     }
     
     /* SCAFFOLDING */
-    fn cast(&self, _dir: Vector3<f64>, _assembly_to_world: &DMatrix<f64>) -> Option<f64> {
-        None
+    fn cast(&self, dir: Vector3<f64>, assembly_to_world: &DMatrix<f64>, pixel_size: f64) -> Option<f64> {
+        let rep = self.representation.with_untracked(|rep| assembly_to_world * rep);
+        if rep[2] < 0.0 {
+            // this constant should be kept synchronized with `point.frag`
+            const POINT_RADIUS_PX: f64 = 4.0;
+            
+            // find the radius of the point in screen projection units
+            let point_radius_proj = POINT_RADIUS_PX * pixel_size;
+            
+            // find the squared distance between the screen projections of the
+            // ray and the point
+            let dir_proj = -dir.fixed_rows::<2>(0) / dir[2];
+            let rep_proj = -rep.fixed_rows::<2>(0) / rep[2];
+            let dist_sq = (dir_proj - rep_proj).norm_squared();
+            
+            // if the ray hits the point, return its depth
+            if dist_sq < point_radius_proj * point_radius_proj {
+                Some(rep[2] / dir[2])
+            } else {
+                None
+            }
+        } else {
+            None
+        }
     }
 }
 
@@ -282,7 +304,7 @@ fn bind_new_buffer_to_attribute(
 }
 
 // the direction in camera space that a mouse event is pointing along
-fn event_dir(event: &MouseEvent) -> Vector3<f64> {
+fn event_dir(event: &MouseEvent) -> (Vector3<f64>, f64) {
     let target: web_sys::Element = event.target().unwrap().unchecked_into();
     let rect = target.get_bounding_client_rect();
     let width = rect.width();
@@ -293,10 +315,13 @@ fn event_dir(event: &MouseEvent) -> Vector3<f64> {
     // `point.vert`
     const FOCAL_SLOPE: f64 = 0.3;
     
-    Vector3::new(
-        FOCAL_SLOPE * (2.0*(f64::from(event.client_x()) - rect.left()) - width) / shortdim,
-        FOCAL_SLOPE * (2.0*(rect.bottom() - f64::from(event.client_y())) - height) / shortdim,
-        -1.0
+    (
+        Vector3::new(
+            FOCAL_SLOPE * (2.0*(f64::from(event.client_x()) - rect.left()) - width) / shortdim,
+            FOCAL_SLOPE * (2.0*(rect.bottom() - f64::from(event.client_y())) - height) / shortdim,
+            -1.0
+        ),
+        FOCAL_SLOPE * 2.0 / shortdim
     )
 }
 
@@ -822,11 +847,11 @@ pub fn Display() -> View {
             },
             on:click=move |event: MouseEvent| {
                 // find the nearest element along the pointer direction
-                let dir = event_dir(&event);
+                let (dir, pixel_size) = event_dir(&event);
                 console::log_1(&JsValue::from(dir.to_string()));
                 let mut clicked: Option<(ElementKey, f64)> = None;
                 for (key, elt) in state.assembly.elements.get_clone_untracked() {
-                    match assembly_to_world.with(|asm_to_world| elt.cast(dir, asm_to_world)) {
+                    match assembly_to_world.with(|asm_to_world| elt.cast(dir, asm_to_world, pixel_size)) {
                         Some(depth) => match clicked {
                             Some((_, best_depth)) => {
                                 if depth < best_depth {